Representations of the compact quantum groupSU q(2) and geometrical quantization

The Souriau—Kostant method of geometrical quantization is used to construct infinite-dimensional irreducible unitary representations of the algebra of functions of the compact quantum groupSU_q(2). The generalization to the case of the quantum groupSU_q(n) is discussed.V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 2, pp. 163–172, August, 1994.