## Unitary genuine principal series of the metaplectic group

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- by Alessandra Pantano, Annegret Paul and Susana A. Salamanca-Riba
- Represent. Theory
**14**(2010), 201-248 - DOI: https://doi.org/10.1090/S1088-4165-10-00367-5
- Published electronically: February 15, 2010
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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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## Bibliographic Information

**Alessandra Pantano**- Affiliation: Department of Mathematics, University of California at Irvine, Irvine, California 92697
- Email: apantano@math.uci.edu
**Annegret Paul**- Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008
- Email: annegret.paul@wmich.edu
**Susana A. Salamanca-Riba**- Affiliation: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003
- Email: ssalaman@nmsu.edu
- 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.
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**14**(2010), 201-248 - MSC (2010): Primary 22E45
- DOI: https://doi.org/10.1090/S1088-4165-10-00367-5
- MathSciNet review: 2593919