Categorical g-actions for modules over truncated shifted Yangians

Abstract: 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 and the theory of symplectic duality/3d mirror symmetry, we expect a categorical g-action on modules for these truncated shifted Yangians. I will explain three results in this direction. First, we have an indirect realization of this action, using equivalences with KLRW-modules. Second, we have a geometric relation between these generalized slices by Hamiltonian reduction. Finally, we have an algebraic version of this Hamiltonian reduction which we are able to relate to the first realization.

representation theory

Audience: researchers in the topic

Comments: This seminar will take place entirely online. Please email Andre Dixon (aldixon@mit.edu) for the Zoom meeting Link.

---

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.

---