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Invariance of $ R$-groups between $ p$-adic inner forms of quasi-split classical groups


Authors: Kwangho Choiy and David Goldberg
Journal: Trans. Amer. Math. Soc. 368 (2016), 1387-1410
MSC (2010): Primary 22E50; Secondary 22E35
DOI: https://doi.org/10.1090/tran/6485
Published electronically: April 3, 2015
MathSciNet review: 3430367
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Abstract: We study the reducibility of parabolically induced representations of non-split inner forms of quasi-split classical groups. The isomorphism of Arthur $ R$-groups, endoscopic $ R$-groups and Knapp-Stein $ R$-groups is established, as well as showing these $ R$-groups are isomorphic to the corresponding ones for the quasi-split form. This shows $ R$-groups are an invariant of the $ L$-packets. The results are applied to classify the elliptic spectrum.


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Additional Information

Kwangho Choiy
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-1058
Email: kwangho.choiy@okstate.edu

David Goldberg
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: goldberg@math.purdue.edu

DOI: https://doi.org/10.1090/tran/6485
Keywords: $R$-groups, $p$-adic inner forms of classical groups, $L$-packets, tempered spectrum, elliptic spectrum
Received by editor(s): October 13, 2013
Received by editor(s) in revised form: May 18, 2014
Published electronically: April 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society