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 $N$.
Silvina Campos
1
,
2
;
José García
1
,
2
;
Linda Saal
1
,
2
1
(1) CIUNSa, Fac. Cs. Exactas, Univ. Nacional de Salta, Argentina
2
(2) CIEM - Univ. Nacional de Córdoba, Argentina
Silvina Campos; José García; Linda Saal. Generalized Gelfand Pairs Attached to some Extensions of Heisenberg Groups. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 507-526. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a2/
@article{JOLT_2025_35_3_a2,
author = {Silvina Campos and Jos\'e Garc{\'\i}a and Linda 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a2/}
}
TY - JOUR
AU - Silvina Campos
AU - José García
AU - Linda Saal
TI - Generalized Gelfand Pairs Attached to some Extensions of Heisenberg Groups
JO - Journal of Lie Theory
PY - 2025
SP - 507
EP - 526
VL - 35
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a2/
ID - JOLT_2025_35_3_a2
ER -
%0 Journal Article
%A Silvina Campos
%A José García
%A Linda Saal
%T Generalized Gelfand Pairs Attached to some Extensions of Heisenberg Groups
%J Journal of Lie Theory
%D 2025
%P 507-526
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a2/
%F JOLT_2025_35_3_a2
