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

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- by David A. Renard and Peter E. Trapa
- Represent. Theory
**4**(2000), 245-295 - DOI: https://doi.org/10.1090/S1088-4165-00-00105-9
- Published electronically: July 31, 2000
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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 $Mp(2n,\mathbb R)$.## References

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## Bibliographic Information

**David A. Renard**- Affiliation: University of Poitiers, Laboratoire de Mathématiques, BP 179, 86960 Futuroscope Cedex, France
- Email: renard@mathlabo.univ-poitiers.fr
**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
- Email: ptrapa@math.ias.edu
- 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 - © Copyright 2000 American Mathematical Society
- Journal: Represent. Theory
**4**(2000), 245-295 - MSC (2000): Primary 22E47; Secondary 22E50
- DOI: https://doi.org/10.1090/S1088-4165-00-00105-9
- MathSciNet review: 1795754