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Representation of Quantum Groups

  • Tetsuya Masuda
  • Katsuhisa Mimachi
  • Yoshiomi Nakagami
  • Masatoshi Noumi
  • Kimio Ueno
Part of the Progress in Mathematics book series (PM, volume 84)

Abstract

The concept of quantum groups is important for the study of the quantum Yang-Baxter equations, Drinfeld [2], Jimbo [4], Manin [5] and others. On the other hand, Woronowicz [10] introduced the concept of compact matrix pseudogroups through the study of the dual object of groups. As pointed out by Rosso in [8], these two concepts are related to each other as quantum Lie algebras and quantum Lie groups. In this talk we want to indicate that the ideas of Kac algebras studied by Takesaki [9] and Enock and Schwartz [3] et al. are helpful for the study of quantum groups. As a result we can give a geometric interpretation for a q-analogue of a certain class of special functions, which has been a long standing problem of q- analogues.

Keywords

Hopf Algebra Quantum Group Haar Measure Casimir Operator Plancherel Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Tetsuya Masuda
    • 1
  • Katsuhisa Mimachi
    • 2
  • Yoshiomi Nakagami
    • 3
  • Masatoshi Noumi
    • 4
  • Kimio Ueno
    • 5
  1. 1.Institute of MathematicsUniversity of TsukubaTsukubaJapan
  2. 2.Department of MathematicsNagoya University Furou-choChikusa-ku, NagoyaJapan
  3. 3.Department of MathematicsYokohama City UniversityYokohamaJapan
  4. 4.Department of MathematicsSophia UniversityTokyoJapan
  5. 5.Department of MathematicsWaseda UniversityTokyoJapan

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