✦ LIBER ✦

Holomorphically Induced Representations of Some Solvable Lie Groups

✍ Scribed by Junko Inoue

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 508 KB
Volume: 186
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3793

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✦ Synopsis

We study holomorphically induced representations r of Lie groups G=exp g from weak polarizations h at f ¥ g*. When G is a connected and simply connected Lie group whose Lie algebra is a normal j-algebra, we obtain a sufficient condition for non-vanishing of r and the decomposition of r into irreducible representations under the assumption that the coadjoint G-orbit G • f is open and h is a positive weak polarization at f.

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