English

Resolutions of tempered representations of reductive p-adic groups

Representation Theory 2013-12-04 v2

Abstract

Let G be a reductive group over a non-archimedean local field and let S(G) be its Schwartz algebra. We compare Ext-groups of tempered G-representations in several module categories: smooth G-representations, algebraic S(G)-modules, bornological S(G)-modules and an exact category of S(G)-modules on LF-spaces which contains all admissible S(G)-modules. We simplify the proofs of known comparison theorems for these Ext-groups, due to Meyer and Schneider-Zink. Our method is based on the Bruhat-Tits building of G and on analytic properties of the Schneider-Stuhler resolutions.

Keywords

Cite

@article{arxiv.1203.1237,
  title  = {Resolutions of tempered representations of reductive p-adic groups},
  author = {Eric Opdam and Maarten Solleveld},
  journal= {arXiv preprint arXiv:1203.1237},
  year   = {2013}
}

Comments

The proof of Theorem 4.2 in the first version was incorrect. In the second version we repaired this and rewrote Section 4

R2 v1 2026-06-21T20:29:47.165Z