TY - JOUR

T1 - Some examples of Hecke algebras for two-dimensional local fields

AU - Braverman, Alexander

AU - Kazhdan, David

PY - 2006

Y1 - 2006

N2 - Let K be a local non-archimedian field, F = K((t)) and let G be & 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 double-struck G sign = G(F) and its central extension G. For instance our spherical Hecke algebra, corresponds to the subgroup G(A) ⊂ G(F) where A ⊂ F is the subring script O signK((t)) where script O sign K ⊂ 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).

AB - Let K be a local non-archimedian field, F = K((t)) and let G be & 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 double-struck G sign = G(F) and its central extension G. For instance our spherical Hecke algebra, corresponds to the subgroup G(A) ⊂ G(F) where A ⊂ F is the subring script O signK((t)) where script O sign K ⊂ 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).

UR - http://www.scopus.com/inward/record.url?scp=33845951232&partnerID=8YFLogxK

U2 - 10.1017/s0027763000009314

DO - 10.1017/s0027763000009314

M3 - Article

AN - SCOPUS:33845951232

VL - 184

SP - 57

EP - 84

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -