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Infinite-dimensional Siegel disc as symplectic and Kaehler quotient

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2504.19931

Author: Tumpach, Alice Barbora

Institutions: Université de Lille, Wolfgang Pauli Institute, Laboratoire Paul Painlevé

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Austrian Science Fund

Award: Geometric Green Learning on Groups and Quotient Spaces

OpenAlex ID: W4416924217

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