Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras

Details Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras

2011-04-20

arxiv.org/abs/1104.4070v2

Mathematics

Representation Theory

Minor corrections to the revised version

Scientific paper

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor together with elementary algebraic and combinatorial arguments to construct "canonical basic sets" in many cases. We will also show that the images of the standard modules through the KZ functor agree with the appropriate cell modules, whenever the Hecke algebra has a cellular structure.

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