An extension of Suzuki's functor to the critical level

Abstract: Suzuki's functor relates the representation theory of the affine Lie algebra to the representation theory of the rational Cherednik algebra in type A. In this talk, we discuss an extension of this functor to the critical level, $t=0$ case. This case is special because the respective categories of representations have large centres. Our main result describes the relationship between these centres, and provides a partial geometric interpretation in terms of Calogero-Moser spaces and opers.

mathematical physicsalgebraic geometryrepresentation theory

Audience: researchers in the topic

Geometric Representation Theory conference

Series comments: Originally planned as a twinned conference held simultaneously at the Max Planck Institute in Bonn, Germany and the Perimeter Institute in Waterloo, Canada. The concept was motivated by the desire to reduce the environmental impact of conference travels. In order to view the talks, register at the website: www.mpim-bonn.mpg.de/grt2020 . The talks from previous days can be be viewed at pirsa.org/C20030 ; slides from the talks are posted here: www.dropbox.com/sh/cjzqbqn7ql8zcjv/AAANB82Hh4t5XDc5RPcZzW0Aa?dl=0