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Transformation groups 2017. Conference dedicated to Prof. Ernest B. Vinberg
on the occasion of his 80th birthday
December 15, 2017 17:50–18:20, Moscow, Skolkovo Institute of Science and Technology
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Sections
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Counting irreducible representations of rational Cherednik algebras of given support
S. Shelley-Abrahamson MIT, USA
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Abstract:
Given a finite complex reflection group $W$ with reflection representation $V$, one can consider the associated rational Cherednik algebra $H_c(W, V)$ and its representation category $O_c(W, V)$, depending on a parameter $c$. The irreducible representations in $O_c(W, V)$ are in natural bijection with the irreducible representations of W, and each representation $M$ in $O_c(W, V)$ has an associated support, a closed subvariety of $V$. Via the $KZ$ functor, the irreducible representations in $O_c(W, V)$ of full support are in bijection with the irreducible representations of the Hecke algebra $H_q(W)$. In the case that $W$ is a finite Coxeter group, I will explain how to count irreducible representations in $O_c(W, V)$ of arbitrary given support by introducing a functor $KZ_L$, generalizing the $KZ$ functor and depending on a finite-dimensional representation $L$ of a rational Cherednik algebra attached to a parabolic subgroup of $W$.
This is joint work with Ivan Losev.
Language: English
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