-
$${{\,\textrm{SO}\,}}(3)$$ -Homogeneous Decomposition of the Flag Scheme of $${{\,\textrm{SL}\,}}_3$$ over $$\mathbb {Z}\left[ 1/2\right] $$ Transform. Groups (IF 0.7) Pub Date : 2024-03-14
Abstract In this paper, we give \(\mathbb {Z}\left[ 1/2\right] \) -forms of \({{\,\textrm{SO}\,}}(3,\mathbb {C})\) -orbits in the flag variety of \({{\,\textrm{SL}\,}}_3(\mathbb {C})\) . We also prove that they give a \(\mathbb {Z}\left[ 1/2\right] \) -form of the \({{\,\textrm{SO}\,}}(3,\mathbb {C})\) -orbit decomposition of the flag variety of \({{\,\textrm{SL}\,}}_3\) .
-
Local Cohomology of Modular Invariant Rings Transform. Groups (IF 0.7) Pub Date : 2024-03-13 Kriti Goel, Jack Jeffries, Anurag K. Singh
For K a field, consider a finite subgroup G of \({\text {GL}}_n(K)\) with its natural action on the polynomial ring \(R:= K[x_1,\dots ,x_n]\). Let \(\mathfrak {n}\) denote the homogeneous maximal ideal of the ring of invariants \(R^G\). We study how the local cohomology module \(H^n_{\mathfrak {n}}(R^G)\) compares with \(H^n_{\mathfrak {n}}(R)^G\). Various results on the a-invariant and on the Hilbert
-
Translation Surfaces in Lie Groups with Constant Gaussian Curvature Transform. Groups (IF 0.7) Pub Date : 2024-03-09 Xu Han, Zhonghua Hou
Let G be an n-dimensional \((n\ge 3)\) Lie group with a bi-invariant Riemannian metric. We prove that if a surface of constant Gaussian curvature in G can be expressed as the product of two curves, then it must be flat. In particular, we can essentially characterize all such surfaces locally in the three-dimensional case.
-
Interval Exchange Transformations Groups: Free Actions and Dynamics of Virtually Abelian Groups Transform. Groups (IF 0.7) Pub Date : 2024-03-02 Nancy Guelman, Isabelle Liousse
-
A Construction of Pseudo-reductive Groups with Non-reduced Root Systems Transform. Groups (IF 0.7) Pub Date : 2024-02-24 Michael Bate, Gerhard Röhrle, Damian Sercombe, David I. Stewart
-
Permawound Unipotent Groups Transform. Groups (IF 0.7) Pub Date : 2024-02-23 Zev Rosengarten
We introduce the class of permawound unipotent groups, and show that they simultaneously satisfy certain “ubiquity” and “rigidity” properties that in combination render them very useful in the study of general wound unipotent groups. As an illustration of their utility, we present two applications: We prove that nonsplit smooth unipotent groups over (infinite) fields finitely generated over \(\textbf{F}_p\)
-
Leavitt Path Algebras in Which Every Lie Ideal is an Ideal and Applications Transform. Groups (IF 0.7) Pub Date : 2024-02-16 Huỳnh Việt Khánh
In this paper, we classify all Leavitt path algebras which have the property that every Lie ideal is an ideal. As an application, we show that Leavitt path algebras with this property provide a class of locally finite, infinite-dimensional Lie algebras whose locally solvable radical is completely determined. This particularly gives us a new class of semisimple Lie algebras over a field of prime characteristic
-
Rationality Problem of Two-Dimensional Quasi-Monomial Group Actions Transform. Groups (IF 0.7) Pub Date : 2024-02-12 Akinari Hoshi, Hidetaka Kitayama
The rationality problem of two-dimensional purely quasi-monomial actions was solved completely by (Hoshi, Kang and Kitayama, J. Algebra 403, 363-400, 2014). As a generalization, we solve the rationality problem of two-dimensional quasi-monomial actions under the condition that the actions are defined within the base field. In order to prove the theorem, we give a brief review of the Severi-Brauer variety
-
On Lie Groups with Conformal Vector Fields Induced by Derivations Transform. Groups (IF 0.7) Pub Date : 2024-02-06
Abstract A pseudo-Riemannian Lie group \((G,\langle \cdot ,\cdot \rangle )\) is a connected and simply connected Lie group with a left-invariant pseudo-Riemannian metric of signature (p, q). This paper is to study pseudo-Riemannian Lie group \((G,\langle \cdot ,\cdot \rangle )\) with conformal vector fields induced by derivations. Firstly, we show that if \(\mathfrak {h}\) is a Cartan subalgebra for
-
Equivariant Fusion Subcategories Transform. Groups (IF 0.7) Pub Date : 2024-02-06 César Galindo, Corey Jones
We provide a parameterization of all fusion subcategories of the equivariantization by a group action on a fusion category. As applications, we classify the Hopf subalgebras of a family of semisimple Hopf algebras of Kac-Paljutkin type and recover Naidu-Nikshych-Witherspoon classification of the fusion subcategories of the representation category of a twisted quantum double of a finite group.
-
Yangian Deformations of $$\mathcal {S}$$ -Commutative Quantum Vertex Algebras and Bethe Subalgebras Transform. Groups (IF 0.7) Pub Date : 2024-02-02
Abstract We construct a new class of quantum vertex algebras associated with the normalized Yang R-matrix. They are obtained as Yangian deformations of certain \(\mathcal {S}\) -commutative quantum vertex algebras, and their \(\mathcal {S}\) -locality takes the form of a single RTT-relation. We establish some preliminary results on their representation theory and then further investigate their braiding
-
Homogeneous Sub-Riemannian Manifolds Whose Normal Extremals are Orbits Transform. Groups (IF 0.7) Pub Date : 2024-02-01 Zaili Yan, Huihui An, Shaoqiang Deng
In this paper, we study homogeneous sub-Riemannian manifolds whose normal extremals are the orbits of one-parameter subgroups of the group of smooth isometries (abbreviated as sub-Riemannian geodesic orbit manifolds). Following Tóth’s approach, we first obtain a sufficient and necessary condition for a homogeneous sub-Riemannian manifold to be geodesic orbit. Secondly, we study left-invariant sub-Riemannian
-
Orbifolds and Manifold Quotients with Upper Curvature Bounds Transform. Groups (IF 0.7) Pub Date : 2024-01-30
Abstract We characterize Riemannian orbifolds with an upper curvature bound in the Alexandrov sense as reflectofolds, i.e., Riemannian orbifolds all of whose local groups are generated by reflections, with the same upper bound on the sectional curvature. Combined with a result by Lytchak–Thorbergsson this implies that a quotient of a Riemannian manifold by a closed group of isometries has locally bounded
-
Divergence Property of the Brown-Thompson Groups and Braided Thompson Groups Transform. Groups (IF 0.7) Pub Date : 2024-01-26 Xiaobing Sheng
-
Permutation Modules with Nakayama Endomorphism Rings Transform. Groups (IF 0.7) Pub Date : 2024-01-25 Xiaogang Li, Jiawei He
Given a field K of characteristic \(p>0\) and a natural number n, assuming that G is a permutation group acting on a set \(\Omega \) with n elements, then \(K\Omega \) is a permutation module for G in the natural way. If G is primitive and \(n\le 5p\), we will show that \(\textrm{End}_{KG}(K\Omega )\) is always a symmetric Nakayama algebra unless \(p=5\) and \(n=25\). As a consequence, \(\textrm{End}_{KG}(K\Omega
-
The Whittaker Functional Is a Shifted Microstalk Transform. Groups (IF 0.7) Pub Date : 2024-01-11 David Nadler, Jeremy Taylor
-
Pauli Matrices and Ring Puzzles Transform. Groups (IF 0.7) Pub Date : 2024-01-04 Sylvain Barré, Mikaël Pichot
-
Ampleness of Normal Bundles of Base Cycles in Flag Domains Transform. Groups (IF 0.7) Pub Date : 2023-12-23 Jaehyun Hong, Aeryeong Seo
-
Quasifold Groupoids and Diffeological Quasifolds Transform. Groups (IF 0.7) Pub Date : 2023-12-19 Yael Karshon, David Miyamoto
Quasifolds are spaces that are locally modelled by quotients of \(\mathbb {R}^n\) by countable affine group actions. These spaces first appeared in Elisa Prato’s generalization of the Delzant construction, and special cases include leaf spaces of irrational linear flows on the torus, and orbifolds. We consider the category of diffeological quasifolds, which embeds in the category of diffeological spaces
-
An Example of Homomorphisms from Guay’s Affine Yangians to Non-rectangular W-algebras Transform. Groups (IF 0.7) Pub Date : 2023-12-18 Mamoru Ueda
We construct a non-trivial homomorphism from the Guay’s affine Yangian associated with \(\widehat{\mathfrak {sl}}(n)\) to the universal enveloping algebra of the W-algebra associated with a Lie algebra \(\mathfrak {gl}(m+n)\) and a nilpotent element of type \((2^{n},1^{m-n})\) for \(m>n\).
-
Factorial Affine $$G_a$$ -Varieties with Height One Plinth Ideals Transform. Groups (IF 0.7) Pub Date : 2023-12-16 Kayo Masuda
Let \(X={\text {Spec}}\;B\) be a factorial affine variety defined over an algebraically closed field k of characteristic zero with a nontrivial action of the additive group \(G_a\) associated to a locally nilpotent derivation \(\delta \) on B. In this article, we study X of dimension \(\ge 3\) under the assumption that the plinth ideal \(\text {pl}(\delta )=\delta (B)\cap A\) is contained in an ideal
-
Galois Closure of a Fivefold Covering and Decomposition of Its Jacobian Transform. Groups (IF 0.7) Pub Date : 2023-12-13 Benjamín M. Moraga
For an arbitrary fivefold ramified covering \(\varvec{f :X\rightarrow Y}\) between compact Riemann surfaces, each possible Galois closure \(\varvec{\hat{f}:\hat{X}\rightarrow Y}\) is determined in terms of the branching data of \(\varvec{f}\). Since \(\varvec{{{\,\textrm{Mon}\,}}(f)}\) acts on \(\varvec{\hat{f}}\), it also acts on the Jacobian variety \(\varvec{{{\,\textrm{J}\,}}(X)}\), and we describe
-
Compact Hyperbolic Coxeter Five-Dimensional Polytopes with Nine Facets Transform. Groups (IF 0.7) Pub Date : 2023-12-11 Jiming Ma, Fangting Zheng
-
The Limit Set for Representations of Discrete Subgroups of $$\text {PU}(1,n)$$ by the Plücker Embedding Transform. Groups (IF 0.7) Pub Date : 2023-12-02 Haremy Zuñiga
Let \(\Gamma \) be a discrete subgroup of \(\text {PU}(1,n)\). In this work, we look at the induced action of \(\Gamma \) on the projective space \(\mathbb {P}(\wedge ^{k+1}\mathbb {C}^{n+1})\) by the Plücker embedding, where \(\wedge ^{k+1}\) denotes the exterior power. We define a limit set for this action called the k-Chen-Greenberg limit set, which extends the classical definition of the Chen-Greenberg
-
Which Schubert Varieties are Hessenberg Varieties? Transform. Groups (IF 0.7) Pub Date : 2023-11-18 Laura Escobar, Martha Precup, John Shareshian
After proving that every Schubert variety in the full flag variety of a complex reductive group G is a general Hessenberg variety, we show that not all such Schubert varieties are adjoint Hessenberg varieties. In fact, in types A and C, we provide pattern avoidance criteria implying that the proportion of Schubert varieties that are adjoint Hessenberg varieties approaches zero as the rank of G increases
-
On the Invariant and Anti-Invariant Cohomologies of Hypercomplex Manifolds Transform. Groups (IF 0.7) Pub Date : 2023-11-17 Mehdi Lejmi, Nicoletta Tardini
A hypercomplex structure (I, J, K) on a manifold M is said to be \(C^\infty \)-pure-and-full if the Dolbeault cohomology \(H^{2,0}_{\partial }(M,I)\) is the direct sum of two natural subgroups called the \(\overline{J}\)-invariant and the \(\overline{J}\)-anti-invariant subgroups. We prove that a compact hypercomplex manifold that satisfies the quaternionic version of the \(dd^c\)-Lemma is \(C^\infty
-
ON THE BRUHAT $$ \mathcal{G} $$ -ORDER BETWEEN LOCAL SYSTEMS ON THE B-ORBITS IN A HERMITIAN SYMMETRIC VARIETY Transform. Groups (IF 0.7) Pub Date : 2023-09-23 MICHELE CARMASSI
Following Lusztig and Vogan, we study the Bruhat G-order on the set \( \mathcal{D} \) of rank 1 local systems on B-orbits in an Hermitian symmetric variety G/L. Supposing Φ irreducible, we obtain a complete combinatorial characterization of the order for Φ of type A, B, D, E and a partial characterization for Φ of type C.
-
A Moment Map for Twisted-Hamiltonian Vector Fields on Locally Conformally Kähler Manifolds Transform. Groups (IF 0.7) Pub Date : 2023-09-20 Daniele Angella, Simone Calamai, Francesco Pediconi, Cristiano Spotti
We extend the classical Donaldson-Fujiki interpretation of the scalar curvature as moment map in Kähler geometry to the wider framework of locally conformally Kähler geometry.
-
Compactifications of Moduli of G-Bundles and Conformal Blocks Transform. Groups (IF 0.7) Pub Date : 2023-09-09 Avery Wilson
For a simple Lie algebra of type A or C and a genus \(g\ge 2\), we show that the conformal blocks algebra on \(\overline{\mathcal {M}}_g\) is finitely generated and relate conformal blocks over singular curves to Schmitt and Muñoz-Castañeda’s compactification of the moduli space of G-bundles.
-
Centralizers of Nilpotent Elements in Basic Classical Lie Superalgebras in Good Characteristic Transform. Groups (IF 0.7) Pub Date : 2023-09-12 Leyu Han
-
Components of $$V(\rho ) \otimes V(\rho )$$ and Dominant Weight Polyhedra for Affine Kac–Moody Lie Algebras Transform. Groups (IF 0.7) Pub Date : 2023-09-05 Sam Jeralds, Shrawan Kumar
Kostant asked the following question: Let \(\mathfrak {g}\) be a simple Lie algebra over the complex numbers. Let \(\lambda \) be a dominant integral weight. Then, \(V(\lambda )\) is a component of \(V(\rho )\otimes V(\rho )\) if and only if \(\lambda \le 2 \rho \) under the usual Bruhat–Chevalley order on the set of weights. In an earlier work with R. Chirivi and A. Maffei, the second author gave
-
Orbit Spaces of Equivariantly Formal Torus Actions of Complexity One Transform. Groups (IF 0.7) Pub Date : 2023-08-31 Anton Ayzenberg, Mikiya Masuda
-
LATTICE VERTEX ALGEBRAS AND LOOP GRASSMANNIANS Transform. Groups (IF 0.7) Pub Date : 2023-08-18 Ivan Mirković
For an integral symmetric matrix κ we construct a new “nonabelian homology localization” of the lattice vertex algebra Lκ on the corresponding loop Grassmannian space 𝒢κ. We attempt to motivate our construction by presenting related topics in the language of “interaction of particles over algebraic curves”.
-
A Friedlander-Suslin Theorem over a Noetherian Base Ring Transform. Groups (IF 0.7) Pub Date : 2023-08-11 Wilberd van der Kallen
Let k be a noetherian commutative ring and let G be a finite flat group scheme over k. Let G act rationally on a finitely generated commutative k-algebra A. We show that the cohomology algebra \(H^*(G,A)\) is a finitely generated k-algebra. This unifies some earlier results: If G is a constant group scheme, then it is a theorem of Evens (Trans. Amer. Math. Soc. 101, 224–239, 1961, Theorem 8.1), and
-
A First Fundamental Theorem of Invariant Theory for the Quantum Queer Superalgebra Transform. Groups (IF 0.7) Pub Date : 2023-08-04 Zhihua Chang, Yongjie Wang
The classical invariant theory for the queer Lie superalgebra is an investigation of the \(\textrm{U}(\mathfrak {q}_n)\)-invariant sub-superalgebra of the symmetric superalgebra \(\textrm{Sym}\left( V^{\oplus r}\oplus V^{*\oplus s}\right) \) for \(V=\mathbb {C}^{n|n}\). We establish a first fundamental theorem of invariant theory in the case that the quantum queer superalgebra \(\text {U}_q(\mathfrak
-
-
FAITHFUL ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON ALGEBRAIC VARIETIES Transform. Groups (IF 0.7) Pub Date : 2023-07-29 VLADIMIR L. POPOV
Considering a certain construction of algebraic varieties X endowed with an algebraic action of the group Aut(Fn), n < ∞, we obtain a criterion for the faithfulness of this action. It gives an infinite family 𝔉 of Xs such that Aut(Fn) embeds into Aut(X). For n ≥ 3, this implies nonlinearity, and for n ≥ 2, the existence of F2 in Aut(X) (hence nonamenability of the latter) for X ∈ 𝔉. We find in 𝔉
-
Classification, Reduction, and Stability of Toric Principal Bundles Transform. Groups (IF 0.7) Pub Date : 2023-07-26 Jyoti Dasgupta, Bivas Khan, Indranil Biswas, Arijit Dey, Mainak Poddar
Let X be a complex toric variety equipped with the action of an algebraic torus T, and let G be a complex linear algebraic group. We classify all T-equivariant principal G-bundles \(\mathcal {E}\) over X and the morphisms between them. When G is connected and reductive, we characterize the equivariant automorphism group \(\text {Aut}_T(\mathcal {E} )\) of \(\mathcal {E}\) as the intersection of certain
-
On the Topological Generation of Exceptional Groups by Unipotent Elements Transform. Groups (IF 0.7) Pub Date : 2023-07-26 Timothy C. Burness
-
HOMFLY-PT HOMOLOGY OF COXETER LINKS Transform. Groups (IF 0.7) Pub Date : 2023-07-22 A. OBLOMKOV, L. ROZANSKY
A Coxeter link is a closure of a product of two braids, one being a quasi-Coxeter element and the other being a product of partial full twists. This class of links includes torus knots Tn, k and torus links Tn, nk. We identify the knot homology of a Coxeter link with the space of sections of a particular line bundle on a natural generalization of the punctual locus inside the flag Hilbert scheme of
-
Jacobians, Anti-Affine Groups and Torsion Points Transform. Groups (IF 0.7) Pub Date : 2023-07-17 A. J. Parameswaran, Amith Shastri K.
We give a criterion for the Jacobian of a singular curve X with at most ordinary n-point singularities to be anti-affine. In particular, for the case of curves with single ordinary double point we exhibit a relation with torsion divisors. If the geometric genus of the singular curve is atleast 3 and the normalization is non-hyperelliptic and non-bielliptic, then except for finitely many cases the Jacobian
-
Quasi-Integrable Modules over Twisted Affine Lie Superalgebras Transform. Groups (IF 0.7) Pub Date : 2023-07-02 Malihe Yousofzadeh
In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that these form a class of not necessarily highest weight modules. We prove that each nonzero level quasi-integrable module is parabolically induced from a cuspidal module, over a finite dimensional Lie superalgebra having a Cartan subalgebra whose corresponding root system just
-
Geometric Vertex Decomposition, Gröbner Bases, and Frobenius Splittings for Regular Nilpotent Hessenberg Varieties Transform. Groups (IF 0.7) Pub Date : 2023-07-03 Sergio Da Silva, Megumi Harada
We initiate a study of the Gröbner geometry of local defining ideals of Hessenberg varieties by studying the special case of regular nilpotent Hessenberg varieties in Lie type A, and focusing on the affine coordinate chart on \({\textrm{Flags}}(\mathbb {C}^n) \cong GL_n(\mathbb {C})/B\) corresponding to the longest element \(w_0\) of the Weyl group \(S_n\) of \(GL_n(\mathbb {C})\). Our main results
-
Tits Groups of Iwahori-Weyl Groups and Presentations of Hecke Algebras Transform. Groups (IF 0.7) Pub Date : 2023-06-29 Radhika Ganapathy, Xuhua He
Let G be a connected reductive group over a non-archimedean local field F and I be an Iwahori subgroup of G(F). Let \(I_n\) is the n-th Moy-Prasad filtration subgroup of I. The purpose of this paper is two-fold: to give some nice presentations of the Hecke algebra of connected, reductive groups with \(I_n\)-level structure; and to introduce the Tits group of the Iwahori-Weyl group of groups G that
-
Topology of Irregular Isomonodromy Times on a Fixed Pointed Curve Transform. Groups (IF 0.7) Pub Date : 2023-06-28 Jean Douçot, Gabriele Rembado
-
On the Induction of p-Cells Transform. Groups (IF 0.7) Pub Date : 2023-06-24 Lars Thorge Jensen, Leonardo Patimo
-
Locally Homogeneous $$C^0$$ -Riemannian Manifolds Transform. Groups (IF 0.7) Pub Date : 2023-06-17 Nina Lebedeva, Artem Nepechiy
We show that locally homogeneous \( C^0\)-Riemannian manifolds are smooth.
-
2-roots for Simply Laced Weyl Groups Transform. Groups (IF 0.7) Pub Date : 2023-06-13 R. M. Green, Tianyuan Xu
-
Crystal Structure on King Tableaux and Semistandard Oscillating Tableaux Transform. Groups (IF 0.7) Pub Date : 2023-06-05 Seung Jin Lee
In 1976, King (1976) defined certain tableaux, that we call King tableaux, to count weight multiplicities of the irreducible representations of the symplectic group Sp(2m). Since crystals are defined, it is an open problem to provide a crystal structure on King tableaux. This paper presents crystal structures on King tableaux and semistandard oscillating tableaux. The semistandard oscillating tableaux
-
ON THE INTEGRAL FORM OF RANK 1 KAC–MOODY ALGEBRAS Transform. Groups (IF 0.7) Pub Date : 2023-05-11 ILARIA DAMIANI, MARGHERITA PAOLINI
In this paper we shall prove that the ℤ-subalgebra generated by the divided powers of the Drinfeld generators \( {x}_r^{\pm } \) (r ∈ ℤ) of the Kac–Moody algebra of type \( {\textrm{A}}_2^{(2)} \) is an integral form (strictly smaller than Mitzman’s; see [Mi]) of the enveloping algebra, we shall exhibit a basis generalizing the one provided in [G] for the untwisted affine Kac–Moody algebras and we
-
On Squares of DEHN Twists About Non-separating Curves of A Non-orientable Closed Surface Transform. Groups (IF 0.7) Pub Date : 2023-05-09 Nao Imoto, Ryoma Kobayashi
-
CALCULATING THE p-CANONICAL BASIS OF HECKE ALGEBRAS Transform. Groups (IF 0.7) Pub Date : 2023-04-13 J. GIBSON, L. T. JENSEN, G. WILLIAMSON
We describe an algorithm for computing the p-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke category inside a semisimple category to build a “model” for indecomposable objects and bases of their morphism spaces. Inside this semisimple category, objects are sequences
-
Modular Tensor Categories, Subcategories, and Galois Orbits Transform. Groups (IF 0.7) Pub Date : 2023-03-31 Julia Plavnik, Andrew Schopieray, Zhiqiang Yu, Qing Zhang
We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion subcategories of modular tensor categories which are closed under the Galois action, and a classification of modular tensor categories which factor as a product of pointed and transitive categories in terms of pseudoinvertible
-
Compatibility of Balanced and SKT Metrics on Two-Step Solvable Lie Groups Transform. Groups (IF 0.7) Pub Date : 2023-03-24 Marco Freibert, Andrew Swann
It has been conjectured by Fino and Vezzoni that a compact complex manifold admitting both a compatible SKT and a compatible balanced metric also admits a compatible Kähler metric. Using the shear construction and classification results for two-step solvable SKT Lie algebras from our previous work, we prove this conjecture for compact two-step solvmanifolds endowed with an invariant complex structure
-
Non-associative Frobenius algebras of type G2 and F4 Transform. Groups (IF 0.7) Pub Date : 2023-03-24 Jari Desmet
-
UNIPOTENT SUBGROUPS OF STABILIZERS Transform. Groups (IF 0.7) Pub Date : 2023-03-23 PHILIPPE GILLE, ROBERT GURALNICK
We consider semicontinuity of certain dimensions on group schemes.
-
STUDY OF PARITY SHEAVES ARISING FROM GRADED LIE ALGEBRAS Transform. Groups (IF 0.7) Pub Date : 2023-03-18 TAMANNA CHATTERJEE
Let G be a complex, connected, reductive, algebraic group, and χ : ℂ× → G be a fixed cocharacter that defines a grading on \( \mathfrak{g} \), the Lie algebra of G. Let G0 be the centralizer of χ(ℂ×). In this paper, we study G0-equivariant parity sheaves on \( \mathfrak{g} \)n, under some assumptions on the field 𝕜 and also assuming two conjectures for the group G. However, both the conjectures are
-
Recognizing the G2-horospherical Manifold of Picard Number 1 by Varieties of Minimal Rational Tangents Transform. Groups (IF 0.7) Pub Date : 2023-03-04 Jun-Muk Hwang, Qifeng Li
Pasquier and Perrin discovered that the G2-horospherical manifold X of Picard number 1 can be realized as a smooth specialization of the rational homogeneous space parameterizing the lines on the 5-dimensional hyperquadric; in other words, it can be deformed nontrivially to the rational homogeneous space. We show that X is the only smooth projective variety with this property. This is obtained as a
-
ALMOST CYCLIC REGULAR SEMISIMPLE ELEMENTS IN IRREDUCIBLE REPRESENTATIONS OF SIMPLE ALGEBRAIC GROUPS Transform. Groups (IF 0.7) Pub Date : 2023-02-20 D. M. TESTERMAN, ALEXANDRE E. ZALESSKI
Let G be a simple linear algebraic group defined over an algebraically closed field of characteristic p ≥ 0 and let ϕ be a nontrivial p-restricted irreducible representation of G. Let T be a maximal torus of G and s ϵ T. We say that s is Ad-regular if α(s) ≠ β(s) for all distinct T-roots α and β of G. Our main result states that if all but one of the eigenvalues of ϕ(s) are of multiplicity 1 then,
-
ON SHEAF COHOMOLOGY FOR SUPERGROUPS ARISING FROM SIMPLE CLASSICAL LIE SUPERALGEBRAS Transform. Groups (IF 0.7) Pub Date : 2023-02-08 DAVID M. GALBAN, DANIEL K. NAKANO
In this paper, the authors study the behavior of the sheaf cohomology functors \( {R}^{\bullet }{\textrm{ind}}_B^G\left(-\right) \) where G is an algebraic group scheme corresponding to a simple classical Lie superalgebra and B is a BBW parabolic subgroup as defined in [GGNW]. We provide a systematic treatment that allows us to study the behavior of these cohomology groups \( {R}^{\bullet }{\textr