Mathematics – Representation Theory
Scientific paper
2003-12-09
Mathematics
Representation Theory
15 pages, revised version
Scientific paper
Let F be a non archimedean local field and G be the locally profinite group GL(N,F), N>0. We denote by X the Bruhat-Tits building of G. For all smooth complex representation V of G and for all level n>0, Schneider and Stuhler have constructed a coefficient system C = C(V, n) on the simplicial complex X. They proved that if V is generated by its fixed vectors under the principal congruence subgroup of level n, then the augmented complex of oriented chains of X with coefficients in C is a resolution of V in the category of smooth complex representations of G. In this paper we give another proof of this result, in the level 0 case, and assuming moreover that V is generated by its fixed vectors under an Iwahori subgroup I of G. Here "level 0" refers to Bushnell and Kutzko's terminology, that is to the case n=1+0. Our approach is different. We strongly use the fact that the trivial character of I is a type in the sense of Bushnell and Kutzko.
No associations
LandOfFree
Acyclicity of Schneider and Stuhler's coefficient systems:another approach in the level 0 case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Acyclicity of Schneider and Stuhler's coefficient systems:another approach in the level 0 case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Acyclicity of Schneider and Stuhler's coefficient systems:another approach in the level 0 case will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-41495