Vol. 306, No. 2, 2020

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Generalized Mullineux involution and perverse equivalences

Thomas Gerber, Nicolas Jacon and Emily Norton

Vol. 306 (2020), No. 2, 487–517
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 𝒪: Losev’s “κ = 0” wall-crossing, and Ringel duality.

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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
Authors
Thomas Gerber
École Polytechnique Fédérale de Lausanne
Lausanne
Switzerland
Nicolas Jacon
UFR Sciences exactes et naturelles, Laboratoire de Mathématiques
Université de Reims Champagne-Ardenne CNRS UMR 9008
Reims
France
Emily Norton
University of Bonn
Bonn
Germany