✦ LIBER ✦

A Geometric Criterion for Gelfand Pairs Associated with Nilpotent Lie Groups

✍ Scribed by Nao Nishihara

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 161 KB
Volume: 183
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3735

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✦ Synopsis

In this paper, we give a proof to the orbit conjecture of Benson Jenkins Lipsman Ratcliff and get a geometric criterion for Gelfand pairs associated with nilpotent Lie groups. Our proof is based on an analysis of the condition by using certain operators naturally attached to two step nilpotent Lie algebras provided with an inner product. A class of nilpotent Lie groups considered by Lauret is also treated as examples.