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DECOMPOSITIONS OF BERNSTEIN–SATO POLYNOMIALS AND SLICES

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Abstract

Let G be a linearly reductive group acting on a vector space V, and f a semi-invariant polynomial on V. In this paper we study systematically decompositions of the Bernstein–Sato polynomial of f in parallel with some representation-theoretic properties of the action of G on V. We provide a technique based on a multiplicity one property, that we use to compute the Bernstein–Sato polynomials of several classical invariants in an elementary fashion. Furthermore, we derive a “slice method” which shows that the decomposition of V as a representation of G can induce a decomposition of the Bernstein–Sato polynomial of f into a product of two Bernstein–Sato polynomials – that of an ideal and that of a semi-invariant of smaller degree. Using the slice method, we compute Bernstein–Sato polynomials for a large class of semi-invariants of quivers.

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  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    ANDRÁS CRISTIAN LŐRINCZ

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LŐRINCZ, A.C. DECOMPOSITIONS OF BERNSTEIN–SATO POLYNOMIALS AND SLICES. Transformation Groups 25, 577–607 (2020). https://doi.org/10.1007/s00031-019-09526-7

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  • DOI: https://doi.org/10.1007/s00031-019-09526-7

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