Generalized Mullineux involution and perverse equivalences

Thomas Gerber, Nicolas Jacon and Emily Norton

Vol. 306 (2020), No. 2, 487–517

DOI: 10.2140/pjm.2020.306.487

Abstract

We define a generalization of the Mullineux involution on multipartitions using the theory of crystals for higher-level Fock spaces. Our generalized Mullineux involution turns up in representation theory via two important derived functors on cyclotomic Cherednik category $\mathcal{𝒪}$: Losev’s “$\kappa =0$” wall-crossing, and Ringel duality.

Keywords

Mullineux involution, Hecke algebra, Cherednik algebra

Mathematical Subject Classification 2010

Primary: 16T30, 17B37, 20C08

Milestones

Received: 5 April 2019

Revised: 16 January 2020

Accepted: 25 January 2020

Published: 13 July 2020