Heisenberg algebras and rational double affine Hecke algebras

Details Heisenberg algebras and rational double affine Hecke algebras Heisenberg algebras and rational double affine Hecke algebras

2010-11-30

arxiv.org/abs/1011.6488v2

Mathematics

Quantum Algebra

57 pages

Scientific paper

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.

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