Unitary representations of type B rational Cherednik algebras and crystal combinatorics

Abstract

Abstract We compare crystal combinatorics of the level $2$ Fock space with the classification of unitary irreducible representations of type B rational Cherednik algebras to study how unitarity behaves under parabolic restriction. We show that the crystal operators that remove boxes preserve the combinatorial conditions for unitarity, and that the parabolic restriction functors categorifying the crystals send irreducible unitary representations to unitary representations. Furthermore, we find the supports of the unitary representations.