A (kind of) monoidal localization theorem for the small quantum group

          @misc{ scivideos_PIRSA:22060012,
            doi = {10.48660/22060012},
            url = {https://pirsa.org/22060012},
            author = {Negron, Cris},
            keywords = {Mathematical physics},
            language = {en},
            title = {A (kind of) monoidal localization theorem for the small quantum group},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060012 see, \url{https://scivideos.org/pirsa/22060012}}
          }
          

Abstract

" I will talk about a monoidal localization theorem for the small quantum group u_q(G), where G is a reductive algebraic group and q is a root of unity. In joint work with Julia Pevtsova, we show that the category of representations for u_q(G) admits a fully faithful tensor embedding into the category of coherent sheaves over a “quantum” flag variety. This quantum flag variety is, essentially, some finitely fibered space over the classical flag variety G/B. I will explain how this embedding theorem codifies certain relationships between the small quantum group and its quantum Borels. "