The isomorphism of the stable representation and the regular representation of the algebra of functions on the quantum group (Q1363861)

The author studies representations of the algebra of functions on the quantum group \(SU_q(2)\). The involution algebra \(A\) of functions on \(SU_q(2)\) is defined for the real \(q\), \(0<|q|<1\), and is generated by the generators \(a\), \(b\), \(c\), \(d\) satisfying the commutation relations \(ab=qba\), \(ac=qca\), \(ad-qcb=1\), \(bc=cb\), \(cd=qdc\), \(bd=qdb\), \(da-q^{-1} bc=1\) with the involute antilinear antihomomorphism *: \(a^*=d\), \(b^*=-qc\). The algebra \(A\) admits the structure of the Hopf algebra with the comultiplication \(\Delta g^j_j= \sum_{k=1,2} g^i_k \otimes g^k_j\). In this work, the author proves that the stable representation \(\prod\) and the regular representation of the algebra of functions on the quantum group \(A= \text{Fun} (SU_q(2))\) are unitary equivalent. [See Theor. Math. Phys. 101, 1269-1280 (1994; Zbl 0852.17011)].