Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

Peng Shan

Annales scientifiques de l'École Normale Supérieure (2011)

  • Volume: 44, Issue: 1, page 147-182
  • ISSN: 0012-9593

Abstract

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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.

How to cite

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Shan, Peng. "Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras." Annales scientifiques de l'École Normale Supérieure 44.1 (2011): 147-182. <http://eudml.org/doc/272214>.

@article{Shan2011,
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.},
author = {Shan, Peng},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Hecke algebra; induction; restriction; crystal; Fock space; categorification},
language = {eng},
number = {1},
pages = {147-182},
publisher = {Société mathématique de France},
title = {Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras},
url = {http://eudml.org/doc/272214},
volume = {44},
year = {2011},
}

TY - JOUR
AU - Shan, Peng
TI - Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2011
PB - Société mathématique de France
VL - 44
IS - 1
SP - 147
EP - 182
AB - 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.
LA - eng
KW - Hecke algebra; induction; restriction; crystal; Fock space; categorification
UR - http://eudml.org/doc/272214
ER -

References

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