Title:Shifted quantum affine algebras and shifted Yangians
Speaker: Oleksandr Tsymbaliuk (Simons Center for Geometry and Physics, Stony Brook University)
Abstract: In this talk, I will speak about shifted quantum affine algebras and shifted Yangians, as well as their incarnations through geometry of parabolic Laumon spaces, affine Grassmannians, and Toda 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 quantum affine algebras, while on the geometric side we replace cohomology by K-theory.
This is a joint work with M. Finkelberg.
Seminar URL: http://research.math.osu.edu/reps/