Homological algebra for Schwartz algebras of reductive p-adic groups

Abstract

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 V and W are two tempered irreducible representations and if V or W is square-integrable, then Ext_G^n(V,W) vanishes for all n>0. We use this to prove in full generality a formula for the formal dimension of square-integrable representations due to Schneider and Stuhler.

34 pages, version 2 contains, in addition, a discussion about formal dimensions from the point of view of Schwartz algebras and von Neumann algebras

References in corpus (4)

• Dualizing the coarse assembly map
• Smooth group representations on bornological vector spaces
• Embeddings of derived categories of bornological modules
• Combable groups have group cohomology of polynomial growth

Cited by in corpus (10)

• Euler characteristics and Gysin sequences for group actions on boundaries
• Combable groups have group cohomology of polynomial growth
• Periodic cyclic homology of affine Hecke algebras
• Duality for Ext-groups and extensions of discrete series for graded Hecke algebras
• The Dixmier-Malliavin Theorem and Bornological Vector Spaces
• Some Fréchet algebras for which the Chern character is an isomorphism
• Extensions of tempered representations
• Periodic cyclic homology of reductive p-adic groups
• Resolutions of tempered representations of reductive p-adic groups
• A formula of Arthur and affine Hecke algebras