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The Genuine Omega-regular Unitary Dual of the Metaplectic Group

Published online by Cambridge University Press:  20 November 2018

Alessandra Pantano ,
Annegret Paul  and
Susana A. Salamanca-Riba
Alessandra Pantano
Affiliation:
Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA e-mail: apantano@uci.edu
Annegret Paul
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA e-mail: annegret.paul@wmich.edu
Susana A. Salamanca-Riba
Affiliation:
Department of Mathematics, New Mexico State University, Las Cruces, NM 88003, USA e-mail: ssalaman@nmsu.edu
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Abstract

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We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group.

Keywords

22E46Metaplectic grouposcillator representationbottom layer mapcohomological inductionParthasarathy’s Dirac Operator Inequalitypseudospherical principal series
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 3 , 01 June 2012 , pp. 669 - 704
Copyright
Copyright © Canadian Mathematical Society 2012

References

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