Supports of simple modules in cyclotomic Cherednik categories O

Abstract

The goal of this paper is to compute the supports of simple modules in the categories $\mathcal{O}$ for the rational Cherednik algebras associated to groups $G(\ell ,1,n)$. For this we compute some combinatorial maps on the set of simples: wall-crossing bijections and a certain ${\mathfrak{sl}}_{\infty }$-crystal associated to a Heisenberg algebra action on a Fock space.

28 pages, v2 30 pages, 5.6 expanded, mistakes fixed; 32 pages, improved exposition, accepted version

References in corpus (2)

• 2-Kac-Moody algebras
• On categories O for quantized symplectic resolutions

Cited by in corpus (10)

• Combinatorial Wall-Crossing and the Mullineux Involution
• W-exponentials, Schur elements, and the support of the spherical representation of the rational Cherednik algebra
• Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution
• On modular categories O for quantized symplectic resolutions
• On Refined Filtration By Supports for Rational Cherednik Categories O
• Heisenberg algebra, wedges and crystals
• Cylindric multipartitions and level-rank duality
• Crystal isomorphisms and wall-crossing maps for rational Cherednik algebras
• Classification of the finite-dimensional unitary representations of type B rational Cherednik algebras
• Decomposition numbers for the principal ${\Phi }_{2n}$-block of ${\mathrm{Sp}}_{4n}(q)$ and ${\mathrm{SO}}_{4n+1}(q)$