Homological Algebra for Schwartz Algebras of Reductive P-adic Groups
نویسنده
چکیده
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 ExtG(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.
منابع مشابه
Representations of Reductive Groups
This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...
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