2005/01/31 by Ralf Meyer
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Mathematics #Pure mathematics #math.RT #msc:18E30 #msc:20G05
paper · pdf · doi:10.1007/978-3-8348-0352-8_13
published as Noncommutative geometry and number theory, Vieweg, 2006, pp. 263-300 · 34 pages, version 2 contains, in addition, a discussion about formal dimensions from the point of view of Schwartz algebras and von Neumann algebras
arxiv created 2005/06/02 · openalex publication_date 2007/12/17 · arxiv updated 2015/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if G is semi-simple, V and W are tempered irreducible representations of G, and V or W is square-integrable, then Ext G n (V, W) ≅ 0 for all n ≥ 1. We use this to prove in full generality a formula for the formal dimension of square-integrable representations due to Schneider and Stuhler.