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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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