Inductive limits of compact quantum groups and their unitary representations

2019/08/12 by Sato, Ryosuke · 2 citations
#FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1908.03988

Abstract

We will introduce the notion of inductive limits of compact quantum groups as W^*-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.

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