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Unitary genuine principal series of the metaplectic group

Authors: Alessandra Pantano, Annegret Paul and Susana A. Salamanca-Riba
Journal: Represent. Theory 14 (2010), 201-248
MSC (2010): Primary 22E45
Published electronically: February 15, 2010
MathSciNet review: 2593919
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Abstract: This paper presents some recent progress on the classification of the unitary genuine irreducible representations of the metaplectic group $Mp(2n)$. Our focus will be on Langlands quotients of genuine minimal principal series; the main result is an embedding of the set of unitary parameters of such representations into the union of spherical unitary parameters for certain split orthogonal groups. The latter are known from work of D. Barbasch; hence we obtain the non-unitarity of a large (conjecturally complete) set of parameters for Langlands quotients of genuine principal series of $Mp(2n)$.

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Additional Information

Alessandra Pantano
Affiliation: Department of Mathematics, University of California at Irvine, Irvine, California 92697

Annegret Paul
Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008

Susana A. Salamanca-Riba
Affiliation: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003

Received by editor(s): May 26, 2009
Published electronically: February 15, 2010
Additional Notes: This research was supported by NSF grants DMS 0554278 and DMS 0201944.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.