Homological algebra for Schwartz algebras of reductive p-adic groups

Details Homological algebra for Schwartz algebras of reductive p-adic groups Homological algebra for Schwartz algebras of reductive p-adic groups

2005-01-31

arxiv.org/abs/math/0501548v2

Mathematics

Representation Theory

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

Scientific paper

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.

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