  We describe a family of coherent states and an associated resolution of the
identity for a quantum particle whose classical configuration space is the
d-dimensional sphere S^d. The coherent states are labeled by points in the
associated phase space T*(S^d). These coherent states are NOT of Perelomov type
but rather are constructed as the eigenvectors of suitably defined annihilation
operators. We describe as well the Segal-Bargmann representation for the
system, the associated unitary Segal-Bargmann transform, and a natural
inversion formula. Although many of these results are in principle special
cases of the results of B. Hall and M. Stenzel, we give here a substantially
different description based on ideas of T. Thiemann and of K. Kowalski and J.
Rembielinski. All of these results can be generalized to a system whose
configuration space is an arbitrary compact symmetric space. We focus on the
sphere case in order to be able to carry out the calculations in a
self-contained and explicit way.
