We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable representations modulo the center. There are many examples of nilpotent Lie groups admitting families of dilations and square-integrable representations. Much less is known about examples admitting square-integrable representations for which the quotient by the center does not admit a family of dilations. In this paper we construct a two-parameter family of characteristically nilpotent Lie groups G(α, β) in dimension 11, admitting square-integrable representations modulo the center Z, such that G(α, β)/Z does not admit a family of dilations.
1
Fakultät für Mathematik, Universität Wien, Wien, Austria
Dietrich Burde; Jordy Timo van Velthoven. Characteristically Nilpotent Lie Groups with Flat Coadjoint Orbits. Journal of Lie Theory, Tome 35 (2025) no. 2, pp. 227-237. http://geodesic.mathdoc.fr/item/JOLT_2025_35_2_a0/
@article{JOLT_2025_35_2_a0,
author = {Dietrich Burde and Jordy Timo van Velthoven},
title = {Characteristically {Nilpotent} {Lie} {Groups} with {Flat} {Coadjoint} {Orbits}},
journal = {Journal of Lie Theory},
pages = {227--237},
year = {2025},
volume = {35},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_2_a0/}
}
TY - JOUR
AU - Dietrich Burde
AU - Jordy Timo van Velthoven
TI - Characteristically Nilpotent Lie Groups with Flat Coadjoint Orbits
JO - Journal of Lie Theory
PY - 2025
SP - 227
EP - 237
VL - 35
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2025_35_2_a0/
ID - JOLT_2025_35_2_a0
ER -
%0 Journal Article
%A Dietrich Burde
%A Jordy Timo van Velthoven
%T Characteristically Nilpotent Lie Groups with Flat Coadjoint Orbits
%J Journal of Lie Theory
%D 2025
%P 227-237
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2025_35_2_a0/
%F JOLT_2025_35_2_a0
