Decomposition of tensor products of modular irreducibles for \SL₂

2002/05/16 by Stephen Doty, Doty, Stephen, Anne Henke +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.math/0205186

arxiv created 2002/05/16 · arxiv updated 2009/11/30

Abstract

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group \SL₂, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands. Various other related results are obtained, and numerous examples are computed.

Cited by

• Odd-primary torsion in the homology of unordered configurations on the torus
• Some formulae relating modular representations of elementary abelian p-groups
• A conjecture on the tensor ideal for an elementary p-group generated by the restriction of a Steinberg module

Related

• Decomposition of tensor products of modular irreducible representations for SL₃ (With an Appendix by C.M. Ringel)
• On certain tilting modules for SL₂ II
• On Certain Tilting Modules for SL2
• Decomposition of Tensor Products of Modular Irreducible Representations for SL₃: the p ≥ 5 case
• Structure of the tensor product of two simple modules of quantum GL₂