Heisenberg algebras and rational double affine Hecke algebras

P. Shan (1) , Eric Vasserot (1)

1 IMJ - Institut de Mathématiques de Jussieu

In this paper we categorify the Heisenberg action on the Fock space via the category O of cyclotomic rational double affine Hecke algebras. This permits us to relate the filtration by the support on the Grothendieck group of O to a representation theoretic grading defined using the Heisenberg action. This implies a recent conjecture of Etingof.

Domaines: Algèbres quantiques [math.QA]

P. Shan, Eric Vasserot. Heisenberg algebras and rational double affine Hecke algebras. 2010. ⟨hal-00540662v2⟩