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Unitary genuine principal series of the metaplectic group
Author(s):
Alessandra
Pantano;
Annegret
Paul;
Susana
A.
Salamanca-Riba
Journal:
Represent. Theory
14
(2010),
201-248.
MSC (2010):
Primary 22E45
Posted:
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  . 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  .
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Additional 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
DOI:
10.1090/S1088-4165-10-00367-5
PII:
S 1088-4165(10)00367-5
Received by editor(s):
May 26, 2009
Posted:
February 15, 2010
Additional Notes:
This research was supported by NSF grants DMS 0554278 and DMS 0201944.
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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