## Distinguished tame supercuspidal representations and odd orthogonal periods

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- by Jeffrey Hakim and Joshua Lansky
- Represent. Theory
**16**(2012), 276-316 - DOI: https://doi.org/10.1090/S1088-4165-2012-00418-6
- Published electronically: June 1, 2012
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## Abstract:

We further develop and simplify the general theory of distinguished tame supercuspidal representations of reductive $p$-adic groups due to Hakim and Murnaghan, as well as the analogous theory for finite reductive groups due to Lusztig. We apply our results to study the representations of $\mathrm {GL}_n(F)$, with $n$ odd and $F$ a nonarchimedean local field, that are distinguished with respect to an orthogonal group in $n$ variables. In particular, we determine precisely when a supercuspidal representation is distinguished with respect to an orthogonal group and, if so, that the space of distinguishing linear forms has dimension one.## References

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## Bibliographic Information

**Jeffrey Hakim**- Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
- MR Author ID: 272088
- Email: jhakim@american.edu
**Joshua Lansky**- Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016
- Email: lansky@american.edu
- Received by editor(s): March 7, 2011
- Received by editor(s) in revised form: November 23, 2011
- Published electronically: June 1, 2012
- Additional Notes: Both authors were supported by NSF grant DMS-0854844.
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**16**(2012), 276-316 - MSC (2010): Primary 22E50, 11F70; Secondary 11F67, 11E08, 11E81
- DOI: https://doi.org/10.1090/S1088-4165-2012-00418-6
- MathSciNet review: 2925798