Representation of Quantum Groups
The concept of quantum groups is important for the study of the quantum Yang-Baxter equations, Drinfeld , Jimbo , Manin  and others. On the other hand, Woronowicz  introduced the concept of compact matrix pseudogroups through the study of the dual object of groups. As pointed out by Rosso in , 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  and Enock and Schwartz  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.
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