Characters of infinite-dimensional quantum classical groups: BCD cases

TL;DR

This paper explores the character theory of infinite-dimensional quantum classical groups, linking quantum algebra representations with probabilistic Markov processes on their duals, advancing understanding of quantum group structures.

Contribution

It clarifies the relationship between quantized universal enveloping algebras and quantized characters, and constructs Markov semigroups on quantum group duals.

Findings

Established connections between Drinfeld-Jimbo algebras and quantized characters.

Constructed Markov semigroups on duals of quantum groups.

Enhanced understanding of infinite-dimensional quantum group representations.

Abstract

We study the character theory of inductive limits of $q$-deformed classical compact groups. In particular, we clarify the relationship between the representation theory of Drinfeld-Jimbo quantized universal enveloping algebras and our previous work on the quantized characters. We also apply the character theory to construct Markov semigroups on unitary duals of $SO_q(2N+1)$, $Sp_q(N)$, and their inductive limits.