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On Induced Representations Distinguished by Orthogonal Groups

Published online by Cambridge University Press:  20 November 2018

Cesar Valverde
Cesar Valverde*
Affiliation:
Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102-1811 e-mail: cvalverd@rutgers.edu
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Abstract.

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Let $F$ be a local non-archimedean field of characteristic zero. We prove that a representation of $GL\left( n,\,F \right)$ obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic.

Keywords

22E50distinguished representationparabolic induction
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 647 - 658
Copyright
Copyright © Canadian Mathematical Society 2013

References

[BlD] Blanc, P. and Delorme, P., Vecteurs distributions H-invariants de représentations induites, pour un espace symétrique réductif p-adique G=H. Ann. Inst. Fourier (Grenoble) 58 (2008, no. 1, 213–261. http://dx.doi.org/10.5802/aif.2349 Google Scholar
[BH] Bushnell, C. and Henniart, G. The local Langlands conjecture for GL(2). Grundlehren der MathematischenWissenschaften, 335, Springer-Verlag, Berlin, 2006.Google Scholar
[FK] Flicker, Y. Z. and Kazhdan, D. A., Metaplectic correspondence. Inst. Hautes E´ tudes Sci. Publ. Math. 64 (1986, 53–110.Google Scholar
[HL] Hakim, J. and Lansky, J., Distinguished tame supercuspidal representations and odd orthogonal periods. arxiv:1108.5114v1Google Scholar
[HM] Hakim, J. and Murnaghan, F., Distinguished tame supercuspidal representations. Int. Math. Res. Pap. IMRP 2008, no. 2, Art. ID rpn005, 166 pp.Google Scholar
[H] Howe, R. E., Tamely ramified supercuspidal representations of GLn(F). Pacific J. Math. 73 (1977, no. 2, 437–460.Google Scholar
[J] Jacquet, H., Représentations distinguées pour le group orthogonal. C. R. Acad. Sci. Paris Sér. I Math. 312 (1991, no. 13, 957–961.Google Scholar
[Mao] Mao, Z., A fundamental lemma for metaplectic correspondence. J. Reine Angew. Math. 496 (1998, 107–129.Google Scholar
[Mat] Matringe, N., Distinguished principal series representations for GLn over a p - adic field. Pacific J. Math. 239 (2009, no. 1, 53–63. http://dx.doi.org/10.2140/pjm.2009.239.53 Google Scholar
[Moy] Moy, A., Local constants and the tame Langlands correspondence. Amer. J. Math. 108(1986, no. 4, 863–930. http://dx.doi.org/10.2307/2374518 Google Scholar
[MVW] Moeglin, C., Vignéras, M.-F. , and Waldspurger, J.-L., Correspondances de Howe sur un corps p-adique. Lecture Notes in Mathematics, 1291, Springer-Verlag, Berlin, 1987.Google Scholar
[Zel] Zelevinsky, A. V., Induced representations of reductive p-adic groups II. On irreducible representations of GL(n). Ann. Sci. Ecole Norm. Sup. (4) 13 (1980, no. 2, 165–210.Google Scholar