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

Renard, David; Trapa, Peter

doi:10.1090/S1088-4165-00-00105-9

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 $Mp(2n,\mathbb R)$.

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