Abstract

abstract:

Given a (complex, smooth) irreducible representation $\pi$ of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation $\sigma$ of a classical group, we show that the (normalized) parabolic induction $\pi\rtimes\sigma$ is reducible if there exists $\rho$ in the supercuspidal support of $\pi$ such that $\rho\rtimes\sigma$ is reducible. In special cases we also give irreducibility criteria for $\pi\rtimes\sigma$ when the above condition is not satisfied.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 505-546
Launched on MUSE
2020-03-24
Open Access
No
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