Double affine Hecke algebras and 2-dimensional local fields

1998/12/03 by Mikhail Kapranov, M. Kapranov, Kapranov, M. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/9812021

28p. plain TEX

arxiv created 1998/12/03 · openalex publication_date 1998/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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((t₁))((t₂)), and J is a certain analog of the Iwahori subgroup.

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