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Iwahori-Hecke Algebras of SL2 over 2-Dimensional Local Fields

Published online by Cambridge University Press:  20 November 2018

Kyu-Hwan Lee
Kyu-Hwan Lee*
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, USA
*
khlee@math.uconn.edu
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Abstract

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In this paper we construct an analogue of Iwahori–Hecke algebras of $\text{S}{{\text{L}}_{2}}$ over 2-dimensional local fields. After considering coset decompositions of double cosets of a Iwahori subgroup, we define a convolution product on the space of certain functions on $\text{S}{{\text{L}}_{2}}$, and prove that the product is well-defined, obtaining a Hecke algebra. Then we investigate the structure of the Hecke algebra. We determine the center of the Hecke algebra and consider Iwahori–Matsumoto type relations.

Keywords

22E5020G25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 6 , 14 December 2010 , pp. 1310 - 1324
Copyright
Copyright © Canadian Mathematical Society 2010

Footnotes

The author was supported in part by EPSRC grant on zeta functions and in part by KOSEF Grant #R01-2003-000-10012-0.

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