Generalized Mullineux involution and perverse equivalences

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.

arXiv commentFinal version. Proof of Proposition 3.3, Lemma 3.10 and Lemma 3.13 rewritten in more detail

References in corpus (7)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• On the category O for rational Cherednik algebras
• Rouquier's conjecture and diagrammatic algebra
• The Blanchet-Khovanov algebras
• Integral presentations of quantum lattice Heisenberg algebras
• Derived equivalences for Rational Cherednik algebras
• Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution