Shan, Peng
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras  [ Cristaux d'espaces de Fock et algèbres de Hecke doublement affines rationnelles cyclotomiques ]
Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 44 (2011) no. 1 , p. 147-182
Zbl 1225.17019 | MR 2760196
doi : 10.24033/asens.2141
URL stable : http://www.numdam.org/item?id=ASENS_2011_4_44_1_147_0

Classification:  20C08
Mots clés: algèbre de Hecke, induction, restriction, cristal, espace de Fock, catégorification
On définit les foncteurs de i-restriction et i-induction sur la catégorie 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.
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.

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