A Jordan-Schwinger Representation of Quadratic Relations for SU_q(2) Operators and of the q-Analog Wigner-Eckart Theorem

Abstract

A q-analog Jordan-Schwinger (QJS) representation is presented which affords q-analog boson operator realizations of Woronowicz’ and Witten’s quadratic relations of quantum group SU_q(2). Emphasis is put on the q-analog Wigner-Eckart theorem. The QJS representation is applied to recursion relations for the Clebsch-Gordan coefficient of SU_q(2). This leads to finding that subalgebras su_q(1, 1) and su_q(2) other than the ordinary su_q(2) are embedded in the QJS representation.