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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Self-dual representations of $\operatorname {SL}(n,F)$
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by Kumar Balasubramanian PDF
Proc. Amer. Math. Soc. 144 (2016), 435-444 Request permission

Abstract:

Let $F$ be a non-Archimedean local field of characteristic $0$ and $G=\operatorname {SL}(n,F)$. Let $(\pi ,W)$ be an irreducible smooth self-dual representation $G$. The space $W$ of $\pi$ carries a non-degenerate $G$-invariant bilinear form $( , )$ which is unique up to scaling. The form $( , )$ is easily seen to be symmetric or skew-symmetric and we set $\varepsilon ({\pi })=\pm 1$ accordingly. In this article, we show that $\varepsilon {(\pi )}=1$ when $\pi$ is an Iwahori spherical representation of $G$.
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Additional Information
  • Kumar Balasubramanian
  • Affiliation: Department of Mathematics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, Madhya Pradesh, India
  • MR Author ID: 1034435
  • Email: bkumar@iiserb.ac.in
  • Received by editor(s): March 24, 2014
  • Received by editor(s) in revised form: December 8, 2014
  • Published electronically: May 28, 2015
  • Communicated by: Pham Huu Tiep
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 435-444
  • MSC (2010): Primary 22-XX
  • DOI: https://doi.org/10.1090/proc12739
  • MathSciNet review: 3415609