Iwahori-Hecke Algebras of SL_2 over 2-dimensional Local Fields

Details Iwahori-Hecke Algebras of SL_2 over 2-dimensional Local Fields Iwahori-Hecke Algebras of SL_2 over 2-dimensional Local Fields

2005-06-07

arxiv.org/abs/math/0506115v3

Mathematics

Representation Theory

Scientific paper

In this paper we construct an analogue of Iwahori-Hecke algebras of 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 SL_2, and prove that the product is well-defined. Then we investigate the structure of the Hecke algebra. We determine the center of the Hecke algebra and consider Iwahori-Matsumoto type relations.

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