Geodesic
Iwahori-Hecke Algebras of SL2 over 2-Dimensional Local Fields
Canadian journal of mathematics, Tome 62 (2010) no. 6, pp. 1310-1324

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DOI

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.
DOI : 10.4153/CJM-2010-072-x
Mots-clés : 22E50, 20G25 
Lee, Kyu-Hwan. Iwahori-Hecke Algebras of SL2 over 2-Dimensional Local Fields. Canadian journal of mathematics, Tome 62 (2010) no. 6, pp. 1310-1324. doi: 10.4153/CJM-2010-072-x
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     title = {Iwahori-Hecke {Algebras} of {SL2} over {2-Dimensional} {Local} {Fields}},
     journal = {Canadian journal of mathematics},
     pages = {1310--1324},
     year = {2010},
     volume = {62},
     number = {6},
     doi = {10.4153/CJM-2010-072-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-072-x/}
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