José M.C. Mourão (Lisbon):
Coherent State Transforms and Generalized Theta Functions
Non-abelian theta functions are natural objects in algebraic
geometry generalizing classical (abelian) theta functions.
However, there does not exist, in the non-abelian case, a general
analytic theory that parallels the one valid for abelian theta
functions.
In an attempt to develop such a theory we consider special
finite dimensional spaces of distributions on compact Lie
groups and study solutions of heat equations with initial
conditions in these subspaces. Using coherent state
transforms for Lie groups these solutions can (at least in some
cases) be related with theta functions.