Coherent State Transforms and Theta Functions

Some aspects of the relations between analytic and geometric properties of theta functions, coherent state transforms for Lie groups, and geometric quantization are reviewed. In this context, the classical theta functions on abelian varieties and nonabelian theta functions for vector bundles on elliptic curves are studied. Some applications of these ideas to rank-2 nonabelian theta functions for genus $g\ge 2$ are also discussed.