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Double affine Hecke algebras and 2-dimensional local fields

Author(s): M. Kapranov
Journal: J. Amer. Math. Soc. 14 (2001), 239-262.
MSC (2000): Primary 20C08; Secondary 20G25
Posted: September 25, 2000
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Abstract:

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: kapranov@math.toronto.edu

DOI: 10.1090/S0894-0347-00-00354-4
PII: S 0894-0347(00)00354-4
Received by editor(s): June 8, 1999
Received by editor(s) in revised form: March 16, 2000 and July 25, 2000
Posted: September 25, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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