# Quantum groups, clusters, and Hamiltonian reduction

### APA

Shapiro, A. (2023). Quantum groups, clusters, and Hamiltonian reduction. Perimeter Institute. https://pirsa.org/23040130

### MLA

Shapiro, Alexander. Quantum groups, clusters, and Hamiltonian reduction. Perimeter Institute, Apr. 13, 2023, https://pirsa.org/23040130

### BibTex

@misc{ pirsa_PIRSA:23040130, doi = {10.48660/23040130}, url = {https://pirsa.org/23040130}, author = {Shapiro, Alexander}, keywords = {Mathematical physics}, language = {en}, title = {Quantum groups, clusters, and Hamiltonian reduction}, publisher = {Perimeter Institute}, year = {2023}, month = {apr}, note = {PIRSA:23040130 see, \url{https://pirsa.org}} }

Alexander Shapiro University of Edinburgh

## Abstract

Cluster structure on a quantum group allows one to work with its positive representations, a special class of modules similar in spirit to principal series representations but closed under tensor multiplication. On the other hand, cluster techniques proved inadequate for the study of finite-dimensional representation theory. I will discuss how one can reconcile positive and finite-dimensional representations into one theory by studying moduli spaces of local systems with non-generic monodromies.

Zoom link: https://pitp.zoom.us/j/97677905324?pwd=Tkxlei9wN1llYVpncHA2cnpYKzlhUT09