Journal of Lie Theory

no. 2
Characteristically Nilpotent Lie Groups with Flat Coadjoint Orbits
Journal of Lie Theory, Volume 35 (2025) no. 2, pp. 227-237
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.
DOI: 10.5802/jolt.1382
Classification: 17A36, 17B30, 22E27
Keywords: Characteristically nilpotent Lie algebras, dilations, flat coadjoint orbits 
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     author = {D. Burde and J. T. 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},
     doi = {10.5802/jolt.1382},
     zbl = {08075071},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1382/}
}
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D. Burde; J. T. van Velthoven. Characteristically Nilpotent Lie Groups with Flat Coadjoint Orbits. Journal of Lie Theory, Volume 35 (2025) no. 2, pp. 227-237. doi: 10.5802/jolt.1382

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