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Heisenberg algebras and rational double affine Hecke algebras


Authors: P. Shan and E. Vasserot
Journal: J. Amer. Math. Soc. 25 (2012), 959-1031
MSC (2010): Primary 06B15, 33D80
Published electronically: April 23, 2012
MathSciNet review: 2947944
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Abstract: We relate the filtration by the support on the Grothendieck group $ [\mathcal {O}]$ of the category $ \mathcal {O}$ of cyclotomic rational double affine Hecke algebras to a representation-theoretic grading on $ [\mathcal {O}]$, defined using the action of an affine Lie algebra and of a Heisenberg algebra on the Fock space. This implies a recent conjecture of Etingof. The proof uses a categorification of the Heisenberg action, which is new, and a categorification of the affine Lie algebra action, which was introduced by the first author in an earlier paper.


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Additional Information

P. Shan
Affiliation: Université Paris 7, UMR CNRS 7586, F-75013 Paris, France
Email: shan@math.jussieu.fr

E. Vasserot
Affiliation: Université Paris 7, UMR CNRS 7586, F-75013 Paris, France
Email: vasserot@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00738-3
Received by editor(s): March 22, 2011
Received by editor(s) in revised form: October 30, 2011, and February 12, 2012
Published electronically: April 23, 2012
Article copyright: © Copyright 2012 American Mathematical Society