On reducibility of 𝑝-adic principal series representations of 𝑝-adic groups

Ban, Dubravka; Hundley, Joseph

doi:10.1090/ert/485

On reducibility of $p$-adic principal series representations of $p$-adic groups
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by Dubravka Ban and Joseph Hundley

Represent. Theory 20 (2016), 249-262

DOI: https://doi.org/10.1090/ert/485

Published electronically: August 17, 2016

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Abstract:

We study the continuous principal series representations of split connected reductive $p$-adic groups over $p$-adic fields. We show that such representations are irreducible when the inducing character lies in a certain cone. This is consistent with a conjecture of Schneider regarding reducibility in the semisimple case.

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