The duality theory of a finite dimensional discrete quantum group

Suppose that H is a finite dimensional discrete quantum group and K is a Hilbert space. This paper shows that if there exists an action gamma of H on L( K) so that L( K) is a modular algebra and the inner product on K is H-invariant, then there is a unique C*-representation theta of H on K supplemented by the gamma: The commutant of theta (H) in L(K) is exactly the H-invariant subalgebra of L( K). As an application, a new proof of the classical Schur-Weyl duality theory of type A is given.Mathematics, AppliedMathematicsSCI(E)4ARTICLE123537-354713