Characteristically nilpotent Lie groups with flat coadjoint orbits
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910779264991232 |
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| author | Burde, Dietrich van Velthoven, Jordy Timo |
| author_facet | Burde, Dietrich van Velthoven, Jordy Timo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_10660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristically nilpotent Lie groups with flat coadjoint orbits Burde, Dietrich van Velthoven, Jordy Timo Representation Theory Rings and Algebras 17A36, 22E27, 17B30 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. |
| title | Characteristically nilpotent Lie groups with flat coadjoint orbits |
| topic | Representation Theory Rings and Algebras 17A36, 22E27, 17B30 |
| url | https://arxiv.org/abs/2408.10660 |