Quaternionic representations of exceptional Lie groups

Hung Yean Loke

Vol. 211 (2003), No. 2, 341–367

DOI: 10.2140/pjm.2003.211.341

Abstract

Let G be a quaternionic real form of an exceptional group of real rank 4. Gross and Wallach show that three representations in the continuation of the quaternionic discrete series are unitarizable (see Gross and Wallach, 1996). In this paper we will determine the restrictions of these representations to certain subgroups of G by computing explicitly the intersections of orbits. In particular we will determine certain compact dual pair correspondences of the minimal representation of G.

Milestones

Received: 13 December 1999

Revised: 9 February 2000

Published: 1 October 2003