Category O and Knizhnik-Zamolodchikov functor for Chrednik algebras of varieties with finite group action

Daniel Thompson (MIT)

Wednesday 9th March, 2016 16:00-17:00 Maths 522

Abstract

Etingof (2004) has defined a sheaf of Cherednik algebras and a Hecke algebra associated to smooth varieties with finite group action, which depend on several parameters. In this setting, we prove that the KZ functor from a certain category of modules for the Cherednik algebra to finite dimensional modules over the Hecke algebra is essentially surjective. Then we begin to use this result to study the analog of category O for Cherednik algebras on Riemann surfaces and on products of elliptic curves. In particular we can give conditions on the parameters under which these categories are nonzero.

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