Infinite-dimensional Siegel disc as symplectic and Kaehler quotient
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910920766128128 |
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| author | Tumpach, Alice Barbora |
| author_facet | Tumpach, Alice Barbora |
| contents | In this paper, we construct the restricted infinite-dimensional Siegel disc as a Marsden-Weinstein symplectic reduced space and as Kaehler quotient of a weak Kaehler manifold. The obtained symplectic form is invariant with respect to the left action of the infinite-dimensional restricted symplectic group and coincides with the Kirillov-Kostant-Souriau symplectic form of the restricted Siegel disc obtained via the identification with an affine coadjoint orbit of the restricted symplectic group, or equivalently with a coadjoint orbit of the universal central extension of the restricted symplectic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite-dimensional Siegel disc as symplectic and Kaehler quotient Tumpach, Alice Barbora Symplectic Geometry Differential Geometry Functional Analysis Operator Algebras 53D17, 70H06, 35F21, 47B99 In this paper, we construct the restricted infinite-dimensional Siegel disc as a Marsden-Weinstein symplectic reduced space and as Kaehler quotient of a weak Kaehler manifold. The obtained symplectic form is invariant with respect to the left action of the infinite-dimensional restricted symplectic group and coincides with the Kirillov-Kostant-Souriau symplectic form of the restricted Siegel disc obtained via the identification with an affine coadjoint orbit of the restricted symplectic group, or equivalently with a coadjoint orbit of the universal central extension of the restricted symplectic group. |
| title | Infinite-dimensional Siegel disc as symplectic and Kaehler quotient |
| topic | Symplectic Geometry Differential Geometry Functional Analysis Operator Algebras 53D17, 70H06, 35F21, 47B99 |
| url | https://arxiv.org/abs/2504.19931 |