Genuine Representations of the Metaplectic Group

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.

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Veröffentlicht in:	Compositio mathematica 1998-08, Vol.113 (1), p.23-66
Hauptverfasser:	ADAMS, JEFFREY, BARBASCH, DAN
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	0010-437X 1570-5846
DOI:	10.1023/A:1000450504919