Characters of infinite-dimensional quantum classical groups: BCD cases

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 $S{O}_q(2N+1)$, $S{p}_q(N)$, and their inductive limits.

16 pages