Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

2008/11/27 by Shan, Peng
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0811.4549

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.

Related

• Crystal bases and simple modules for Hecke algebras of type G(p,p,n)
• Heisenberg algebras and rational double affine Hecke algebras
• Two maps on affine type A crystals and Hecke algebras
• Finite dimensional Hecke algebras
• Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A