Partitions, quantum group actions and rigidity

Abstract: In this talk, I will present a new combinatorial approach to the study of ergodic actions of compact quantum groups. The connection between compact quantum groups and the combinatorics of partitions goes back to Banica's founding work on the representation theory of free orthogonal quantum groups, and was later formalized in the seminal paper of Banica and Speicher under the theory of "easy quantum groups". Based on some new alternative version of the Tannaka-Krein reconstruction procedure for ergodic actions, we extend Banica and Speicher's combinatorial approach to the setting of ergodic actions of compact quantum groups. Our examples in particular recovers actions on finite spaces, on embedded homogeneous spaces and on quotient spaces. Moreover, we use this categorical point of view to study the quantum rigidity of ergodic actions on classical spaces, and show that the free quantum groups cannot act ergodically on a classical connected compact space, thereby answering a question of D. Goswami and H. Huang.

The talk is based on the recent preprint arXiv:2112.07506 jointly with Amaury Freslon and Frank Taipe.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.