Journal of Lie Theory 18 (2008), No. 3, 503--515
Copyright Heldermann Verlag 2008
Generalized Gelfand Pairs Associated to Heisenberg Type Groups
Fernando Levstein
Facultad de Matemática, Astronomía y Física, Universidad Nacional, 5000 Córdoba, Argentina
levstein@famaf.unc.edu.ar
Linda Saal
Facultad de Matemática, Astronomía y Física, Universidad Nacional, 5000 Córdoba, Argentina
saal@famaf.unc.edu.ar
[Abstract-pdf]
Let ${\frak N}={\frak Z}\oplus V$ be the Lie algebra corresponding to a group of Heisenberg type N. Assume that $V$ is an irreducible Clifford module. In this article we determine the generalized Gelfand pairs $(K,{\rm N})$, where $K$ is the group of automorphisms of $\frak N$ that preserve $V$.
Keywords: Gelfand pair, group of type H.
MSC: 43A80; 17B10
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