Journal of Lie Theory

no. 3
Generalized Gelfand Pairs Attached to some Extensions of Heisenberg Groups
Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 507-526
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 $N$.
DOI: 10.5802/jolt.1394
Classification: 43A80, 22E27
Keywords: Generalized Gelfand pairs, metaplectic representation 
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     author = {S. Campos and J. Garcia and L. Saal},
     title = {Generalized {Gelfand} {Pairs} {Attached} to some {Extensions} of {Heisenberg} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {507--526},
     year = {2025},
     volume = {35},
     number = {3},
     doi = {10.5802/jolt.1394},
     zbl = {08103099},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1394/}
}
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S. Campos; J. Garcia; L. Saal. Generalized Gelfand Pairs Attached to some Extensions of Heisenberg Groups. Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 507-526. doi: 10.5802/jolt.1394

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