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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The residual spectrum of an inner form of $ Sp_8$ supported in the minimal parabolic subgroup


Author: Neven Grbac
Journal: Trans. Amer. Math. Soc. 361 (2009), 3977-4012
MSC (2000): Primary 11F70; Secondary 22E55
Published electronically: March 13, 2009
MathSciNet review: 2500875
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Abstract: The part of the residual spectrum of an inner form of the split group $ Sp_8$ supported in the minimal parabolic subgroup is decomposed. Since the considered inner form is not quasi-split, the normalization of the standard intertwining operators, required for the calculation of the poles of the Eisenstein series, is out of the reach of the Langlands-Shahidi method. Hence, a normalization technique, based on the transfer of the Plancherel measure between the split group and its inner form, is applied. The obtained decomposition reveals certain features of the residual spectrum of the inner form which do not appear for the split group.


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Additional Information

Neven Grbac
Affiliation: Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
Email: neven.grbac@zpm.fer.hr, neven.grbac@math.uniri.hr

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04853-3
PII: S 0002-9947(09)04853-3
Received by editor(s): April 16, 2007
Published electronically: March 13, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.