Coherent State Transforms and Vector Bundles on Elliptic Curves

Details Coherent State Transforms and Vector Bundles on Elliptic Curves Coherent State Transforms and Vector Bundles on Elliptic Curves

2002-06-25

arxiv.org/abs/math/0206269v3

Mathematics

Algebraic Geometry

small misprints corrected

Scientific paper

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.

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