Multiplicity-free representations of certain nilpotent Lie groups over Siegel domains of the second kind
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913521356242944 |
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| author | Arashi, Koichi |
| author_facet | Arashi, Koichi |
| contents | We investigate the multiplicity-freeness property for the holomorphic multiplier representations of affine transformation groups of a Siegel domain of the second kind. We deal with the generalized Heisenberg group and its subgroups. Necessary and sufficient conditions for a specific representation to be multiplicity-free are provided. We study the multiplicity-freeness property in relation to the geometrical notions of coisotropic action and visible action, and also the commutativity of the algebra of invariant differential operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07262 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multiplicity-free representations of certain nilpotent Lie groups over Siegel domains of the second kind Arashi, Koichi Representation Theory Primary: 22E27, Secondary: 32M05, 53C55 We investigate the multiplicity-freeness property for the holomorphic multiplier representations of affine transformation groups of a Siegel domain of the second kind. We deal with the generalized Heisenberg group and its subgroups. Necessary and sufficient conditions for a specific representation to be multiplicity-free are provided. We study the multiplicity-freeness property in relation to the geometrical notions of coisotropic action and visible action, and also the commutativity of the algebra of invariant differential operators. |
| title | Multiplicity-free representations of certain nilpotent Lie groups over Siegel domains of the second kind |
| topic | Representation Theory Primary: 22E27, Secondary: 32M05, 53C55 |
| url | https://arxiv.org/abs/2205.07262 |