We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
REPRESENTATIONS LISSES p-TEMPÉRÉES DES GROUPES p-ADIQUES.
- Authors
Dat, J.-F.
- Abstract
Abstract. We consider certain asymptotic properties of smooth p-adically valued functions and representations of a p-adic reductive group G. First, we continue the study of the so-called ptempered and p-discrete representations, as defined in a former paper, and apply this to get a classification of "locally integral" representations, i.e., those representations such that for any open compact subgroup H, the H-invariant subspace admits Hecke-invariant lattices. Then we show that the space of square-integrable smooth functions, as defined in the text, is an algebra under convolution to which the action of the Hecke algebra on any p-tempered representation extends naturally. We formulate a Plancherel-like formula but prove it only for SL(2).
- Subjects
P-adic analysis; FUNCTIONAL analysis; DIFFERENTIAL equations; SMOOTHNESS of functions; HECKE algebras; GROUP algebras; HILBERT space
- Publication
American Journal of Mathematics, 2009, Vol 131, Issue 1, p227
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.0.0041