Comultiplications on cohomological Hall algebras and vertex algebras

          @misc{ scivideos_PIRSA:19020062,
            doi = {10.48660/19020062},
            url = {https://pirsa.org/19020062},
            author = {Zhao, Gufang},
            keywords = {Mathematical physics},
            language = {en},
            title = {Comultiplications on cohomological Hall algebras and vertex algebras},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020062 see, \url{https://scivideos.org/index.php/pirsa/19020062}}
          }
          

Abstract

In this talk we will explore a factorization structure of the cohmological Hall algebra (COHA) of a quiver, and the occurrence of the same structure from Beilinson-Drinfeld Grassmannians. In particular, in collaboration with Mirkovic and Yang, we identified a Drinfeld-type comultiplication on the COHA with the factorizable line bundle on the zastava space. I will discuss one aspect of a recent joint work with Rapcak, Soibelman, and Yang, which can be reviewed as a construction of a vertex algebra from the standard comultiplication on the double COHA of the Jordan quiver. The standard comultiplication differs from the Drinfeld comultiplication by an S-operator. The relevant vertex algebra is the VOA at the corner of Rapcak-Gaiotto.