Quantum groups, clusters, and Hamiltonian reduction


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


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


          @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


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