Coherent State Transforms and Vector Bundles on Elliptic Curves
代数几何
2021-10-19 v3 高能物理 - 理论
微分几何
泛函分析
摘要
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.
引用
@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}
}
备注
small misprints corrected