Double affine Hecke algebras and 2-dimensional local fields

Details Double affine Hecke algebras and 2-dimensional local fields Double affine Hecke algebras and 2-dimensional local fields

1998-12-03

arxiv.org/abs/math/9812021v1

Mathematics

Algebraic Geometry

28p. plain TEX

Scientific paper

We give an interpretation of the double affine Hecke algebra of Cherednik as the (suitably regularized) algebra of double cosets of a group G by a subgroup J, extending the well known interpretations of finite and affine Hecke algebras. In this interpretation, G consists of K-points of a split reductive group where K is a 2-dimensional local field such as Q_p((t)) or F_q((t_1))((t_2)), and J is a certain analog of the Iwahori subgroup.

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