Title

ON THE HUMPHREYS CONJECTURE ON SUPPORT VARIETIES OF TILTING MODULES

Document Type

Article

Publication Date

9-15-2019

Abstract

Let G be a simply-connected semisimple algebraic group over an algebraically closed field of characteristic p, assumed to be larger than the Coxeter number. The “support variety” of a G-module M is a certain closed subvariety of the nilpotent cone of G, defined in terms of cohomology for the first Frobenius kernel G . In the 1990s, Humphreys proposed a conjectural description of the support varieties of tilting modules; this conjecture has been proved for G = SL in earlier work of the second author. In this paper, we show that for any G, the support variety of a tilting module always contains the variety predicted by Humphreys, and that they coincide (i.e., the Humphreys conjecture is true) when p is sufficiently large. We also prove variants of these statements involving “relative support varieties.” 1 n

Publication Source (Journal or Book title)

Transformation Groups

First Page

597

Last Page

657

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