Quantum Riemann surfaces: II. The discrete series

We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of ^*-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional ^*-algebras.Supported by DOE under Grant DE-FG02-88ER25065.