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# Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators

Published:2009-06-01
Printed: Jun 2009
• Xiaoxiang Yu
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## Abstract

Suppose that $P=MN$ is a maximal parabolic subgroup of a quasisplit, connected, reductive classical group $G$ defined over a non-Archimedean field and $A$ is the standard intertwining operator attached to a tempered representation of $G$ induced from $M$. In this paper we determine all the cases in which $\Lie(N)$ is prehomogeneous under $\Ad(m)$ when $N$ is non-abelian, and give necessary and sufficient conditions for $A$ to have a pole at $0$.
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 20G05 - Representation theory