Some remarks on the ring of twisted tilting modules for algebraic groups

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JournalJournal of Algebra
DatePublished - 1 Jun 2009
Issue number11
Volume321
Number of pages17
Pages (from-to)3128-3144
Original languageEnglish

Abstract

In a recent paper [S. Doty, A. Henke, Decomposition of tensor products of modular irreducibles for SL2, Q. J. Math. 56 (2005) 189-207], Doty and Henke give a decomposition of the tensor product of two rational simple modules for the special linear group of degree 2 over an algebraically closed field of characteristic p > 0. In performing this calculation it proved useful to know that the simple modules arc twisted tensor products of tilting modules. It seems natural therefore to consider the ring of twisted tilting modules for a semisimple group G (a subring of the representation ring of G). However, we quickly specialize to the case in which G is the special linear group of degree 2. We show that (in this case) the ring is reduced and describe associated varieties. We give formulas from which one may determine the multiplicities of the indecomposable module summands of the tensor product of twisted tilting modules. (C) 2008 Elsevier Inc. All rights reserved.

    Research areas

  • Rational modules, Twisted tilting modules, Character formulas, Special linear group

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