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.References
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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