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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
DOI: https://doi.org/10.1090/ert/485
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
Email: dban@siu.edu

Joseph Hundley
Affiliation: 244 Mathematics Building, University at Buffalo, Buffalo, New York 14260-2900
Email: jahundle@buffalo.edu

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