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 G is semi-simple, V and W are tempered irreducible representations of G, and V or W is square-integrable, then Ext n G (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.
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Meyer, R. (2006). Homological algebra for Schwartz algebras of reductive p-adic groups. In: Consani, C., Marcolli, M. (eds) Noncommutative Geometry and Number Theory. Aspects of Mathematics. Vieweg. https://doi.org/10.1007/978-3-8348-0352-8_13
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DOI: https://doi.org/10.1007/978-3-8348-0352-8_13
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