  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.
