Inductive limits of compact quantum groups and their unitary representations

Abstract

We will introduce the notion of inductive limits of compact quantum groups as $W^{\ast }$-bialgebras equipped with some additional structures. We also formulate their unitary representation theories. Those give a more explicit representation-theoretic meaning to our previous study of quantized characters associated with a given inductive system of compact quantum groups. As a byproduct, we will give an explicit representation-theoretic interpretation to some transformations that play an important role in the analysis of $q$-central probability measures on the paths in the Gelfand-Tsetlin graph.

17 pages, second version (added an appendix)

Cited by in corpus (2)

• Traces On Diagram Algebras I: Free Partition Quantum Groups, Random Lattice Paths And Random Walks On Trees
• Macdonald polynomials and extended Gelfand-Tsetlin graph