Double affine Hecke algebras and 2-dimensional local fields

Kapranov, M.

doi:10.1090/S0894-0347-00-00354-4

Double affine Hecke algebras and 2-dimensional local fields

Author: M. Kapranov
Journal: J. Amer. Math. Soc. 14 (2001), 239-262
MSC (2000): Primary 20C08; Secondary 20G25
DOI: https://doi.org/10.1090/S0894-0347-00-00354-4
Published electronically: September 25, 2000
MathSciNet review: 1800352
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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 by a subgroup $\mathcal F$ , extending the well-known interpretations of the finite and affine Hecke algebras. In this interpretation, consists of -points of a simple algebraic group, where is a 2-dimensional local field such as $\mathbf Q_p((t))$ or , and $\mathcal F$ is a certain analog of the Iwahori subgroup.

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