The duality theory of a finite dimensional discrete quantum group

Lining Jiang; Maozheng Guo; Min Qian

doi:10.1090/S0002-9939-04-07397-6

The duality theory of a finite dimensional discrete quantum group

Lining Jiang^*, Maozheng Guo, Min Qian

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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 γ 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 θ of ℋ on K supplemented by the γ. The commutant of θ (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.

Original language	English
Pages (from-to)	3537-3547
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	132
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9939-04-07397-6
Publication status	Published - Dec 2004

Keywords

C*-homomorphism
Discrete quantum group
Duality

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10.1090/S0002-9939-04-07397-6

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N2 - 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 γ 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 θ of ℋ on K supplemented by the γ. The commutant of θ (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.

AB - 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 γ 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 θ of ℋ on K supplemented by the γ. The commutant of θ (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.

KW - C-homomorphism

KW - Discrete quantum group

KW - Duality

UR - https://www.scopus.com/pages/publications/10044250838

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SP - 3537

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

The duality theory of a finite dimensional discrete quantum group

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