Transactions of the American Mathematical Society

The residual spectrum of an inner form of

supported in the minimal parabolic subgroup

Author(s): Neven Grbac
Journal: Trans. Amer. Math. Soc. 361 (2009), 3977-4012.
MSC (2000): Primary 11F70; Secondary 22E55
Posted: March 13, 2009
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Abstract: The part of the residual spectrum of an inner form of the split group

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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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: 10.1090/S0002-9947-09-04853-3
PII: S 0002-9947(09)04853-3
Received by editor(s): April 16, 2007
Posted: March 13, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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