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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Heisenberg algebras and rational double affine Hecke algebras
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by P. Shan and E. Vasserot PDF
J. Amer. Math. Soc. 25 (2012), 959-1031 Request permission

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
  • 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
  • © Copyright 2012 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 25 (2012), 959-1031
  • MSC (2010): Primary 06B15, 33D80
  • DOI: https://doi.org/10.1090/S0894-0347-2012-00738-3
  • MathSciNet review: 2947944