Super Kähler structures on the complex Abelian Lie supergroups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910575487877120 |
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| author | Chuah, Meng-Kiat Gavarini, Fabio |
| author_facet | Chuah, Meng-Kiat Gavarini, Fabio |
| contents | We consider a real Abelian Lie supergroup $G$ acting on its complexification $M$, equipped with a $G$-invariant super Kähler form. We extend the scheme of classical geometric quantization to this setting and construct a unitary $G$-representation. We show that the occurrences of its irreducible subrepresentations are governed by the image of the moment map of the super Kähler form. As an application, we construct a Gelfand model of $G$, namely a unitary $G$-representation in which every unitary irreducible representation occurs exactly once. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00444 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Super Kähler structures on the complex Abelian Lie supergroups Chuah, Meng-Kiat Gavarini, Fabio Differential Geometry 53 (Primary) We consider a real Abelian Lie supergroup $G$ acting on its complexification $M$, equipped with a $G$-invariant super Kähler form. We extend the scheme of classical geometric quantization to this setting and construct a unitary $G$-representation. We show that the occurrences of its irreducible subrepresentations are governed by the image of the moment map of the super Kähler form. As an application, we construct a Gelfand model of $G$, namely a unitary $G$-representation in which every unitary irreducible representation occurs exactly once. |
| title | Super Kähler structures on the complex Abelian Lie supergroups |
| topic | Differential Geometry 53 (Primary) |
| url | https://arxiv.org/abs/2312.00444 |