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arXiv · 2504.19931

Infinite-dimensional Siegel disc as symplectic and Kaehler quotient

Alice Barbora Tumpach
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Abstract

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.

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Alice Barbora Tumpach. 2025-04-28. Infinite-dimensional Siegel disc as symplectic and Kaehler quotient. https://arxiv.org/abs/2504.19931

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