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Higher Jones Algebras and their Simple Modules

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Abstract

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.

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Acknowledgments

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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  1. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China

    Henning Haahr Andersen

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  1. Henning Haahr Andersen
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Correspondence to Henning Haahr Andersen.

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Andersen, H.H. Higher Jones Algebras and their Simple Modules. Algebr Represent Theor 23, 393–419 (2020). https://doi.org/10.1007/s10468-018-09853-5

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