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Irreducible Genuine Characters of the Metaplectic Group: Kazhdan-Lusztig Algorithm and Vogan Duality

Authors: David A. Renard and Peter E. Trapa
Journal: Represent. Theory 4 (2000), 245-295
MSC (2000): Primary 22E47; Secondary 22E50
Published electronically: July 31, 2000
MathSciNet review: 1795754
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Abstract: We establish a Kazhdan-Lusztig algorithm to compute characters of irreducible genuine representations of the (nonlinear) metaplectic group with half-integral infinitesimal character. We then prove a character multiplicity duality theorem for representations of $Mp(2n,\mathbb R)$ at fixed half-integral infinitesimal character. This allows us to extend some of Langlands’ ideas to $Mp(2n,\mathbb R)$.

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Additional Information

David A. Renard
Affiliation: University of Poitiers, Laboratoire de Mathématiques, BP 179, 86960 Futuroscope Cedex, France

Peter E. Trapa
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540
Address at time of publication: Department of Mathematics, Harvard University, Cambridge, MA 02138

Received by editor(s): November 12, 1999
Received by editor(s) in revised form: April 28, 2000
Published electronically: July 31, 2000
Additional Notes: The first author acknowledges the support of NSF grant DMS97-29992 and the Ellentuck Fund of the Institute for Advanced Study
The second author acknowledges the support of NSF grant DMS97-29995
Article copyright: © Copyright 2000 American Mathematical Society