An approximate equivalence for the GNS representation of the Haar state of SUq(2).

We use the crystallised C ∗ -algebra C (S U q (2)) at q = 0 to obtain a unitary that gives an approximate equivalence involving the GNS representation on the L 2 space of the Haar state of the quantum SU(2) group and the direct integral of all the infinite dimensional irreducible representations of the C ∗ -algebra C (S U q (2)) for nonzero values of the parameter q. This approximate equivalence gives a KK class via the Cuntz picture in terms of quasihomomorphisms as well as a Fredholm representation of the dual quantum group S U q (2) ^ with coefficients in a C ∗ -algebra in the sense of Mishchenko. [ABSTRACT FROM AUTHOR]