The duality theory of a finite dimensional discrete quantum group
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- by Lining Jiang, Maozheng Guo and Min Qian PDF
- Proc. Amer. Math. Soc. 132 (2004), 3537-3547 Request permission
Abstract:
Suppose that $\mathcal {H}$ is a finite dimensional discrete quantum group and $K$ is a Hilbert space. This paper shows that if there exists an action $\gamma$ of $\mathcal {H}$ on $L(K)$ so that $L(K)$ is a modular algebra and the inner product on $K$ is $\mathcal {H}$-invariant, then there is a unique C*-representation $\theta$ of $\mathcal {H}$ on $K$ supplemented by the $\gamma .$ The commutant of $\theta \left ( \mathcal {H}\right )$ in $L(K)$ is exactly the $\mathcal {H}$-invariant subalgebra of $L(K)$. As an application, a new proof of the classical Schur-Weyl duality theory of type A is given.References
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Additional Information
- Lining Jiang
- Affiliation: Department of Mathematics, Beijing Institute of Technology, Beijing (100081), People’s Republic of China
- Email: jiangjln@sina.com
- Maozheng Guo
- Affiliation: Department of Mathematics, Peking University, Beijing (100871), People’s Republic of China
- Email: maguo@pku.edu.cn
- Min Qian
- Affiliation: Department of Mathematics, Peking University, Beijing (100871), People’s Republic of China
- Received by editor(s): November 28, 2001
- Received by editor(s) in revised form: December 25, 2002
- Published electronically: July 14, 2004
- Additional Notes: This project was supported by the National Natural Science Foundation of China (10301004)
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3537-3547
- MSC (2000): Primary 46L05; Secondary 16W30
- DOI: https://doi.org/10.1090/S0002-9939-04-07397-6
- MathSciNet review: 2084075