Journal of Lie Theory 35 (2025), No. 3, 507--526
Copyright Heldermann Verlag 2025
Generalized Gelfand Pairs Attached to some Extensions of Heisenberg Groups
Silvina Campos
(1) CIUNSa, Fac. Cs. Exactas, Univ. Nacional de Salta, Argentina
(2) CIEM - Univ. Nacional de Córdoba, Argentina
silvinacampos@exa.unsa.edu.ar
José García
(1) CIUNSa, Fac. Cs. Exactas, Univ. Nacional de Salta, Argentina
(2) CIEM - Univ. Nacional de Córdoba, Argentina
joseigarcia@exa.unsa.edu.ar
Linda Saal
(1) CIUNSa, Fac. Cs. Exactas, Univ. Nacional de Salta, Argentina
(2) CIEM - Univ. Nacional de Córdoba, Argentina
saal@mate.uncor.edu.ar
[Abstract-pdf]
We show new examples of generalized Gelfand pairs of the form $(K,N)$ by considering a family of 3-step nilpotent Lie groups $N:=S\ltimes H$, where $H$ is the $(2n+1)$ dimensional Heisenberg group, $S$ is the subgroup of $(n\times n)$ symmetric matrices and $K$ is a non compact, unimodular subgroup of automorphism of $N$. Also, we determine the automorphism group of $N$.
Keywords: Generalized Gelfand pairs, metaplectic representation.
MSC: 43A80; 22E27.
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