Integration over Compact Quantum Groups

@article{Banica2007IntegrationOC,
  title={Integration over Compact Quantum Groups},
  author={Teodor Banica and Benoit Collins},
  journal={Publications of The Research Institute for Mathematical Sciences},
  year={2007},
  volume={43},
  pages={277-302}
}
  • T. Banica, B. Collins
  • Published 10 November 2005
  • Mathematics
  • Publications of The Research Institute for Mathematical Sciences
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures. 
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73 Citations
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73 Citations

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References

SHOWING 1-10 OF 39 REFERENCES
Integration over quantum permutation groups
Quantum Symmetry Groups of Finite Spaces
Abstract:We determine the quantum automorphism groups of finite spaces. These are compact matrix quantum groups in the sense of Woronowicz. Dedicated to Marc A. Rieffel on the occasion of his…
Quantum Groups and Fuss--Catalan Algebras
Abstract: The categories of representations of compact quantum groups of automorphisms of certain inclusions of finite dimensional ℂ*-algebras are shown to be isomorphic to the categories of…
The boundary of universal discrete quantum groups, exactness, and factoriality
We study the C -algebras and von Neumann algebras associated with the universal discrete quantum groups. They give rise to full prime factors and simple exact C -algebras. The main tool in our work…
Free products of compact quantum groups
We construct and study compact quantum groups from free products ofC*-algebras. In this connection, we discover two mysterious classes of natural compact quantum groups,Au(m) andAo(m). TheAu(m)'s…
Corepresentation theory of universal cosovereign Hopf algebras
We determine the corepresentation theory of universal cosovereign Hopf algebras, for generic matrices over an algebraically closed field of characteristic zero.
A categorical and diagrammatical approach to Temperley-Lieb algebras
Algebraic basics on Temperley-Lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.
Twisted SU (2) group. An example of a non-commutative differential calculus
Pour un nombre ν de l'intervalle [−1, 1], on introduit et on etudie une C*-algebre A engendree par deux elements α et γ satisfaisant une relation de commutation simple dependante de ν
Representations of compact quantum groups and subfactors
Abstract We associate Popa systems (= standard invariants of subfactors) to the finite dimensional representations of compact quantum groups. We characterise the systems arising in this way: these…
Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum Groups
We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These…
...
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