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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Klyachko models of $p$-adic special linear groups
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by Joshua M. Lansky and C. Ryan Vinroot PDF
Proc. Amer. Math. Soc. 139 (2011), 2271-2279 Request permission

Abstract:

We study Klyachko models of $\mathrm {SL}(n, F)$, where $F$ is a non- Archimedean local field. In particular, using results of Klyachko models for $\mathrm {GL}(n, F)$ due to Heumos, Rallis, Offen and Sayag, we give statements of existence, uniqueness, and disjointness of Klyachko models for admissible representations of $\mathrm {SL}(n, F)$, where the uniqueness and disjointness are up to specified conjugacy of the inducing character, and the existence is for unitarizable representations in the case $F$ has characteristic $0$. We apply these results to relate the size of an $L$-packet containing a given representation of $\mathrm {SL}(n, F)$ to the type of its Klyachko model, and we describe when a self-dual unitarizable representation of $\mathrm {SL}(n, F)$ is orthogonal and when it is symplectic.
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Additional Information
  • Joshua M. Lansky
  • Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
  • Email: lansky@american.edu
  • C. Ryan Vinroot
  • Affiliation: Department of Mathematics, College of William and Mary, P. O. Box 8795, Williamsburg, Virginia 23187
  • Email: vinroot@math.wm.edu
  • Received by editor(s): September 3, 2009
  • Received by editor(s) in revised form: June 10, 2010
  • Published electronically: November 29, 2010
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2271-2279
  • MSC (2000): Primary 22E50
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10640-8
  • MathSciNet review: 2775404