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# A Künneth Theorem for $p$-Adic Groups

Published:2007-09-01
Printed: Sep 2007
• A. Raghuram
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## Abstract

Let $G_1$ and $G_2$ be $p$-adic groups. We describe a decomposition of ${\rm Ext}$-groups in the category of smooth representations of $G_1 \times G_2$ in terms of ${\rm Ext}$-groups for $G_1$ and $G_2$. We comment on ${\rm Ext}^1_G(\pi,\pi)$ for a supercuspidal representation $\pi$ of a $p$-adic group $G$. We also consider an example of identifying the class, in a suitable ${\rm Ext}^1$, of a Jacquet module of certain representations of $p$-adic ${\rm GL}_{2n}$.
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 18G15 - Ext and Tor, generalizations, Kunneth formula [See also 55U25] 55U25 - Homology of a product, Kunneth formula

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