Higher Jones Algebras and their Simple Modules
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Let G be a connected reductive algebraic group over a field of positive characteristic p and denote by \(\mathcal T\) the category of tilting modules for G. The higher Jones algebras are the endomorphism algebras of objects in the fusion quotient category of \(\mathcal T\). We determine the simple modules and their dimensions for these semisimple algebras as well as their quantized analogues. This provides a general approach for determining various classes of simple modules for many well-studied algebras such as group algebras for symmetric groups, Brauer algebras, Temperley–Lieb algebras, Hecke algebras and BMW-algebras. We treat each of these cases in some detail and give several examples.
KeywordsTilting modules Cellular algebras Group algebras for symmetric groups Hecke algebras Brauer algebras BMW-algebras
Mathematics Subject Classification (2010)20C20 17B37 20G05 20C30
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Thanks to the referee for a quick and careful reading as well as for her/his many useful comments and corrections.
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