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Suppose that D is a C∗-discrete quantum group and D0 a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a Dmodule algebra, and if the inner product on the Hilbert space H is Dinvariant, there is a unique C∗-representation θ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of θ(D) in L(H).

REPRESENTATION AND DUALITY OF UNIMODULAR C*-DISCRETE QUANTUM GROUPS

REPRESENTATION AND DUALITY OF UNIMODULAR C^*-DISCRETE QUANTUM GROUPS