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Journal of the American Mathematical Society

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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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Double affine Hecke algebras and 2-dimensional local fields
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by M. Kapranov PDF
J. Amer. Math. Soc. 14 (2001), 239-262 Request permission


We give an interpretation of the double affine Hecke algebra of Cherednik as a (suitably regularized) algebra of double cosets of a group $G$ by a subgroup $\mathcal F$, extending the well-known interpretations of the finite and affine Hecke algebras. In this interpretation, $G$ consists of $K$-points of a simple algebraic group, where $K$ is a 2-dimensional local field such as $\mathbf Q_p((t))$ or $F_q((t_1))((t_2))$, and $\mathcal F$ is a certain analog of the Iwahori subgroup.
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Additional Information
  • M. Kapranov
  • Affiliation: Department of Mathematics, University of Toronto, 100 St. George St., Toronto, Ontario, Canada M5S 3G3
  • Email:
  • Received by editor(s): June 8, 1999
  • Received by editor(s) in revised form: March 16, 2000, and July 25, 2000
  • Published electronically: September 25, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 239-262
  • MSC (2000): Primary 20C08; Secondary 20G25
  • DOI:
  • MathSciNet review: 1800352