Some examples of Hecke algebras over 2-dimensional local fields

2005/10/25 by Alexander Braverman, David Kazhdan, Braverman, Alexander +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0510538

openalex publication_date 2005/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a local non-archimedian field, F=K((t)) and let G be a split semi-simple group. The purpose of this paper is to study certain analogs of spherical (and Iwahori) Hecke algebras for representations of the group G(F) and its central extension by means of K*. For instance our spherical Hecke algebra corresponds to the subgroup G(A) where A is the subring \calO_K((t)) where \calO_K⊂ K is the ring of integers. It turns out that for generic level the spherical Hecke algebra is trivial; however, on the critical level it is quite large. On the other hand we expect that the size of the corresponding Iwahori-Hecke algebra does not depend on a choice of a level (details will be considered in another publication).

Citations

• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

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