Coulomb branches and representation theory

Presentation Date: 

Sunday, June 12, 2022

Location: 

Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification, Northeastern University, Boston

Presentation Slides: 

Coulomb branches of quiver gauge theories are a type of almost commutative algebra arising from 3d quantum field theory.  These include many popular algebras, like universal enveloping algebras, W-algebras and Cherednik algebras of type A.  Realizing these algebras as Coulomb branches emphasizes the role of a commutative subalgebra (generalizing the Gelfand-Tsetlin subalgebra of the universal enveloping algebra), and analyzing the representation theory of these algebras with respect to these commutative subalgebras naturally gives rise to flavoured KLRW algebras.  I'll try to explain the connection between these algebras and what this tells us about their representation theory.