Infinite-dimensional Siegel disc as symplectic and Kaehler quotient
Symplectic Geometry
2025-04-29 v1 Differential Geometry
Functional Analysis
Operator Algebras
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.
Keywords
Cite
@article{arxiv.2504.19931,
title = {Infinite-dimensional Siegel disc as symplectic and Kaehler quotient},
author = {Alice Barbora Tumpach},
journal= {arXiv preprint arXiv:2504.19931},
year = {2025}
}