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Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators
Published online by Cambridge University Press: 20 November 2018
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 $\text{Ad}\left( m \right)$ when $N$ is non-abelian, and give necessary and sufficient conditions for $A$ to have a pole at $0$.
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- Copyright © Canadian Mathematical Society 2009
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