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Regular version of the site

Article

On refined filtration by supports for rational Cherednik categories O

Selecta Mathematica, New Series. 2018. Vol. 24. No. 2. P. 1729-1804.
Losev Ivan, Shelley-Abrahamson S.

For a complex reflection group W with reflection representation hh, we define and study a natural filtration by Serre subcategories of the category O_c(W,h) of representations of the rational Cherednik algebra H_c(W,h). This filtration refines the filtration by supports and is analogous to the Harish-Chandra series appearing in the representation theory of finite groups of Lie type. Using the monodromy of the Bezrukavnikov–Etingof parabolic restriction functors, we show that the subquotients of this filtration are equivalent to categories of finite-dimensional representations over generalized Hecke algebras. When W is a finite Coxeter group, we give a method for producing explicit presentations of these generalized Hecke algebras in terms of finite-type Iwahori–Hecke algebras. This yields a method for counting the number of irreducible objects in O_c(W,h) of given support. We apply these techniques to count the number of irreducible representations in O_c(W,h) of given support for all exceptional Coxeter groups W and all parameters c, including the unequal parameter case. This completes the classification of the finite-dimensional irreducible representations of O_c(W,h) for exceptional Coxeter groups W in many new cases.