SU(2)Q IN A HILBERT-SPACE OF ANALYTIC-FUNCTIONS

The algebra SU(2)q is realized in a Hilbert space H(q)2 of analytic functions; the starting point is the differential realization of operators that satisfy q-algebra in a Hilbert space H(q). The Weyl realization of SU(2)q is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2 x 2 linear representation of SU(2)q is obtained as consistency conditions for coupling j1 = j2 = 1/2 to j = 0, 1; the derivation of Clebsch-Gordan coefficients is sketched and the q-generalization of the rotation matrices is included. The unitary correspondence of H(q) with a Hilbert space of complex functions of a real variable is also studied. The study presented in this paper follows Bargmann's formalism for the rotation group as closely as possible.