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Representation Theory

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

Authors: Dubravka Ban and Joseph Hundley
Journal: Represent. Theory 20 (2016), 249-262
MSC (2010): Primary 22E50, 11S80
Published electronically: August 17, 2016
MathSciNet review: 3537231
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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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Additional Information

Dubravka Ban
Affiliation: Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901
MR Author ID: 658785

Joseph Hundley
Affiliation: 244 Mathematics Building, University at Buffalo, Buffalo, New York 14260-2900
MR Author ID: 746477

Keywords: $p$-adic representations, $p$-adic groups, principal series
Received by editor(s): February 20, 2016
Received by editor(s) in revised form: June 7, 2016
Published electronically: August 17, 2016
Additional Notes: This research was supported by NSA grant H98230-15-1-0234
Article copyright: © Copyright 2016 American Mathematical Society