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The duality theory of a finite dimensional discrete quantum group |
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| Authors: | Lining Jiang Maozheng Guo Min Qian |
| Institution: | Department of Mathematics, Beijing Institute of Technology, Beijing (100081), People's Republic of China ; Department of Mathematics, Peking University, Beijing (100871), People's Republic of China ; Department of Mathematics, Peking University, Beijing (100871), People's Republic of China |
| Abstract: | Suppose that  is a finite dimensional discrete quantum group and  is a Hilbert space. This paper shows that if there exists an action  of  on  so that  is a modular algebra and the inner product on  is  -invariant, then there is a unique C*-representation  of  on  supplemented by the  The commutant of  in  is exactly the  -invariant subalgebra of  . As an application, a new proof of the classical Schur-Weyl duality theory of type A is given. |
| Keywords: | Discrete quantum group C*-homomorphism duality |
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