  We consider the problem of a central spin with arbitrary spin s that
interacts pairwise and uniformly with a bath of N spins with s=1/2. We present
two approaches for determining the exact spectrum of this model, one based on
properties of SU(2), and the other based on integrability. We also analyze the
exact time evolution of a spin coherent state, and compute the time evolution
of various quantities of physical interest, including the entanglement entropy,
spin polarization and Loschmidt echo.
