Coherent State Transforms and Vector Bundles on Elliptic Curves
Algebraic Geometry
2021-10-19 v3 High Energy Physics - Theory
Differential Geometry
Functional Analysis
Abstract
We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift k -> k+n appears in a natural way in this finite-dimensional framework.
Cite
@article{arxiv.math/0206269,
title = {Coherent State Transforms and Vector Bundles on Elliptic Curves},
author = {C. Florentino and J. Mourao and J. P. Nunes},
journal= {arXiv preprint arXiv:math/0206269},
year = {2021}
}
Comments
small misprints corrected