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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Intertwining maps between $p$-adic principal series of $p$-adic groups
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by Dubravka Ban and Joseph Hundley PDF
Represent. Theory 25 (2021), 975-993 Request permission

Abstract:

In this paper we study $p$-adic principal series representation of a $p$-adic group $G$ as a module over the maximal compact subgroup $G_0$. We show that there are no non-trivial $G_0$-intertwining maps between principal series representations attached to characters whose restrictions to the torus of $G_0$ are distinct, and there are no non-scalar endomorphisms of a fixed principal series representation. This is surprising when compared with another result which we prove: that a principal series representation may contain infinitely many closed $G_0$-invariant subspaces. As for the proof, we work mainly in the setting of Iwasawa modules, and deduce results about $G_0$-representations by duality.
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Additional Information
  • Dubravka Ban
  • Affiliation: School of Mathematical and Statistical Sciences, 1245 Lincoln Drive, Southern Illinois University, Carbondale, Illinois 62901
  • MR Author ID: 658785
  • Email: dban@siu.edu
  • Joseph Hundley
  • Affiliation: Department of Mathematics, 244 Mathematics Building, University at Buffalo, Buffalo, New York 14260-2900
  • MR Author ID: 746477
  • Email: jahundle@buffalo.edu
  • Received by editor(s): May 2, 2020
  • Received by editor(s) in revised form: December 11, 2020
  • Published electronically: December 1, 2021
  • Additional Notes: The work on this project was partially supported by Simons Foundation Collaboration Grant 428319
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 975-993
  • MSC (2020): Primary 22E50
  • DOI: https://doi.org/10.1090/ert/571
  • MathSciNet review: 4346019