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Genuine Representations of the Metaplectic Group

Published online by Cambridge University Press:  04 December 2007

JEFFREY ADAMS  and
DAN BARBASCH
JEFFREY ADAMS
Affiliation:
University of Maryland, Department of Maryland, Department of Mathematics, College Park, MD 20742, U.S.A.
DAN BARBASCH
Affiliation:
Cornell University, Department of Mathematics, Ithaca N.Y. 14853, U.S.A.
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Abstract

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This paper determines the θ–correspondence for the dual pairs (O(p, q), Sp(2n, R)) when p+q=2n+1. As a consequence, there is a natural bijection between genuine irreducible representations of the metaplectic group Mp(2n, R) and irreducible representations of SO(p, q) with p+q=2n+1.

Type
Research Article
Information
Compositio Mathematica , Volume 113 , Issue 1 , August 1998 , pp. 23 - 66
Copyright
© 1998 Kluwer Academic Publishers