Characters of infinite-dimensional quantum classical groups: BCD cases

2021/06/24 by Sato, Ryosuke
#FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2106.12771

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.

Related

• Inductive limits of compact quantum groups and their unitary representations
• Type classification of extremal quantized characters
• Markov semigroups on unitary duals generated by quantized characters
• Characters of Representations of Quantum Groups of Type A_n
• q-deformed Character Theory for Infinite-Dimensional Symplectic and Orthogonal Groups