A Kunneth theorem for p-adic groups

Abstract

Let G₁ and G₂ be p-adic groups. We describe a decomposition of Ext-groups in the category of smooth representations of G₁ × G₂ in terms of Ext-groups for G₁ and G₂. We comment on Ext¹_G(π, π) for a supercuspidal representation π of a p-adic group G. We also consider an example of identifying the class, in a suitable Ext₁, of a Jacquet module of certain representations of p-adic GL_2n.