Multiplicative characters and Gaussian fluctuation limits

TL;DR

This paper extends the concept of multiplicative characters to inductive limit quantum groups, provides explicit examples for quantum unitary groups, and establishes a Gaussian fluctuation limit theorem based on this framework.

Contribution

It introduces a new formulation of multiplicativity for inductive limit quantum groups and demonstrates a Gaussian fluctuation limit theorem using this concept.

Findings

Explicit examples of multiplicative characters for quantum unitary groups

Formulation of multiplicativity for inductive limit quantum groups

Gaussian fluctuation limit theorem established

Abstract

It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples of multiplicative characters in the case of quantum unitary groups. Furthermore, we show a Gaussian fluctuation limit theorem using this concept of multiplicativity.