Steinberg squares and tensor products of tilting modules with simple modules

2018/12/17 by Paul Sobaje, Sobaje, Paul
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1812.06711

openalex publication_date 2018/12/17 · openalex created_date 2018/12/22 · openalex updated_date 2026/07/28

Abstract

Let G be a simple and simply connected algebraic group over an algebraically closed field \Bbbk of characteristic p>0. We establish an isomorphism of G-modules between a direct sum of modules St ⊗ St and a direct sum of tensor products of simple modules of restricted highest weight with tilting modules that are projective over the Frobenius kernel of G. This isomorphism holds precisely when Donkin's Tilting Module Conjecture does, and thus can be seen as providing a G-module theoretic characterization of this conjecture.

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