Alexander Tsymbaliuk (Simons Center) Shifted affine quantum groups and shifted Yangians
In this talk, I will speak about the shifted affine quantum groups and shifted Yangians, as well as their incarnations through geometry of parabolic Laumon spaces, affine Grassmannians, additive/multiplicative slices, and Todda lattice.
The shifted Yangians were originally introduced by Brundan-Kleshchev in the gl(n) case with a dominant shift and were later generalized by Kamnitzer-Webster-Weekes-Yacobi to any simple Lie algebra with an arbitrary shift. These algebras attracted recently a new interest due to their interplay with the Coulomb branches.
In the first half of the talk, I will remind those results about shifted Yangians, while the second part will be devoted to the multiplicative analogue of this story. On the algebraic side this leads to the notion of shifted affine quantum groups, while on the geometric side we replace cohomology by K-theory and additive slices are replaced by multiplicative slices.
This is a joint project with M. Finkelberg.