Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

[Cristaux d'espaces de Fock et algèbres de Hecke doublement affines rationnelles cyclotomiques]

Shan, Peng

Annales scientifiques de l'École Normale Supérieure, Tome 44 (2011), p. 147-182 / Harvested from Numdam

Résumé

On définit les foncteurs de $i$-restriction et $i$-induction sur la catégorie $\mathcal {O}$ des algèbres de Hecke doublement affines rationnelles cyclotomiques. Ceci donne lieu à un cristal sur l’ensemble des classes d’isomorphismes de modules simples, qui est isomorphe au cristal d’un espace de Fock.

Abstract

We define the $i$-restriction and $i$-induction functors on the category $\mathcal {O}$ 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.

Détail

Publié le : 2011-01-01

MR 2760196 | Zbl 1225.17019

DOI : https://doi.org/10.24033/asens.2141
Classification:  20C08
Mots clés: algèbre de Hecke, induction, restriction, cristal, espace de Fock, catégorification

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