Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

TL;DR

This paper constructs a crystal structure on the simple modules of cyclotomic rational double affine Hecke algebras, linking it to Fock space crystals, and introduces new functors for their categorification.

Contribution

It defines i-restriction and i-induction functors on category O, establishing a crystal isomorphism with Fock space crystals, advancing the categorification of these algebraic structures.

Findings

Established a crystal structure on simple modules

Defined new i-restriction and i-induction functors

Proved isomorphism with Fock space crystals

Abstract

We define the i-restriction and i-induction functors on the category O of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.