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On the Representation Theory of some Noncrossing Partition Quantum Groups

  • Amaury FreslonEmail author
Article

Abstract

We compute the representation theory of two families of noncrossing partition quantum groups connected to amalgamated free products and free wreath products. This illustrates the efficiency of the methods developed in our previous joint work with M. Weber.

Keywords

Compact quantum groups Representation theory Noncrossing partitions 

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References

  1. 1.
    Banica, T., Speicher, R.: Liberation of orthogonal Lie groups. Adv. Math. 222 4, 1461–1501 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bichon, T.: Free wreath product by the quantum permutation group. Algebr. Represent. Theory 7(4), 343–362 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Freslon, A.: On the partition approach to Schur-Weyl duality and free quantum group. Transform. Groups 22(3), 705–751 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Freslon, A.: On two-coloured noncrossing partition quantum groups, Arxiv preprint (2017)Google Scholar
  5. 5.
    Freslon, A., Weber, M.: On the representation theory of partition (easy) quantum groups. J. Reine Angew. Math. 720, 155–197 (2016)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Lemeux, F.: Fusion rules for some free wreath product quantum groups and application. J. Funct. Anal. 267(7), 2507–2550 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Wang, S.: Free products of compact quantum groups. Comm. Math. Phys. 167(3), 671–692 (1995)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques d’OrsayUniversitë Paris-Sud, CNRS, Université Paris-SaclayOrsayFrance

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