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Some Examples of Hecke Algebras for Two-Dimensional Local Fields

Published online by Cambridge University Press:  11 January 2016

Alexander Braverman  and
David Kazhdan
Alexander Braverman
Affiliation:
Einstein Institute of MathematicsEdmond J. Safra campus, Hebrew University of JerusalemGivat-Ram, 91904 JerusalemIsraelbraval@math.brown.edu
David Kazhdan
Affiliation:
Mathematics DepartmentBox 1917Brown UniversityProvidence, RI 02912U.S.A.kazhdan@math.huji.ac.il
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Abstract

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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 = G(F) and its central extension Ĝ. For instance our spherical Hecke algebra corresponds to the subgroup G (A) ⊂ G(F) where A ⊂ F is the subring OK((t)) where OK ⊂ K is the ring of integers. It turns out that for generic level (cf. [4]) 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).

Keywords

22E5522E67
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 183 , 2006 , pp. 57 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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