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ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES

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Abstract

Given a connected reductive complex algebraic group G and a spherical subgroup H ⊂ G, the extended weight monoid \( {\hat{\Lambda}}_G^{+}\left(G/H\right) \) encodes the G-module structures on spaces of global sections of all G-linearized line bundles on G/H. Assuming that G is semisimple and simply connected and H is specified by a regular embedding in a parabolic subgroup P ⊂ G, in this paper we obtain a description of \( {\hat{\Lambda}}_G^{+}\left(G/H\right) \) via the set of simple spherical roots of G/H together with certain combinatorial data explicitly computed from the pair (P;H). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing \( {\hat{\Lambda}}_G^{+}\left(G/H\right) \) in the case where H is strongly solvable.

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  1. National Research University”Higher School of Economics”, Moscow, Russia

    ROMAN AVDEEV

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To the memory of my teacher Ernest Borisovich Vinberg

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AVDEEV, R. ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES. Transformation Groups 26, 403–431 (2021). https://doi.org/10.1007/s00031-021-09642-3

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