Type classification of extremal quantized characters

TL;DR

This paper classifies the types of von Neumann factors generated by extremal quantized characters in the context of quantum unitary groups, extending the understanding of quantum group representations in operator algebras.

Contribution

It provides a complete classification of the von Neumann factor types arising from extremal quantized characters of quantum unitary groups $U_q(N)$.

Findings

Classifies von Neumann factor types for extremal quantized characters

Extends representation theory to quantum groups in operator algebra context

Provides a comprehensive solution for quantum unitary groups $U_q(N)$

Abstract

The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the representation associated with any extremal quantized character generates von Neumann factor. In the viewpoint of operator algebras (and measurable dynamical systems), it is natural to ask what is the Murray-von Neumann-Connes type of the resulting factor. In this paper, we give a complete solution to this question when the inductive system is of quantum unitary groups $U_q(N)$.