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# Iwahori--Hecke Algebras of $SL_2$ over $2$-Dimensional Local Fields

Published:2010-09-15
Printed: Dec 2010
• Kyu-Hwan Lee,
Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, USA
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## Abstract

In this paper we construct an analogue of Iwahori--Hecke algebras of $\operatorname{SL}_2$ 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 $\operatorname{SL}_2$, 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.
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 20G25 - Linear algebraic groups over local fields and their integers

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