Generalized Mullineux involution and perverse equivalences

TL;DR

This paper introduces a generalized Mullineux involution on multipartitions using crystal theory, linking it to derived functors in representation theory such as wall-crossing and Ringel duality.

Contribution

It extends the Mullineux involution to multipartitions via crystal theory, connecting it to key derived functors in cyclotomic Cherednik category O.

Findings

Generalized Mullineux involution defined for multipartitions

Connection established between involution and wall-crossing functors

Link between involution and Ringel duality in representation theory

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 the Ringel duality.