Seminar on Combinatorics, Lie Theory, ​and Topology

Levi restriction for Coulomb branch algebras and categorical $\mathfrak{g}$-actions for truncated shifted Yangians

by Joel Kamnitzer (University of Toronto, Canada)


​Given a representation $V$ of a reductive group $G$, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction.  This variety comes with a natural deformation quantization, called a Coulomb branch algebra.  Important cases of these Coulomb branches are (generalized) affine Grassmannian slices, and their quantizations are truncated shifted Yangians.  Motivated by the geometric Satake correspondence, we define a categorical $\mathfrak{g}$-action on modules for these truncated shifted Yangians.  Our main tool is the study of how the Coulomb branch algebra changes when we pass from $G$, $V$ to $L$, $U$, where $L$ is a Levi in $G$ and $U$ is the invariants for a coweight defining $L$.

Click here for the slides of the talk and here to see the video of the talk.