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Restrictions of Quaternionic Representations

✍ Scribed by Hung Yean Loke

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 202 KB
Volume: 172
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3450

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✦ Synopsis

In a paper by Gross and Wallach [1996, J. Reine Angew. Math. 481, 73 123] the K-types of the continuations of the quaternionic discrete series of a quaternionic Lie group G are associated with projective orbits O of certain subgroups in G(C). In this paper, we will show that the restrictions of the representations to quaternionic subgroups are closely related with the intersection of the Zariski closure of O with hyperplanes. We apply this to the minimal representations of the exceptional groups of real rank 4 and investigate the correspondences of certain compact dual pairs.

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