Tuesday, March 26, 2019 — 2:30 PM EDT

Ben Webster, Department of Pure Mathematics, University of Waterloo

"Coulomb, Galois, Gelfand-Tsetlin"

In the grand tradition of naming objects after mathematicians who knew nothing about them, I'll talk a bit about Galois orders, their Gelfand-Tsetlin modules, and how most important examples are Coulomb branches.

To expand a bit: the universal enveloping algebra U(gl_n) contains a copy of a polynomial ring in (n+1)n/2 variables, called the Gelfand-Tsetlin subalgebra (which were implicit in work of Gelfand and Tsetlin).  Remarkably, if you tensor with the fraction field of this subalgebra, the universal enveloping algebra comes surprisingly close to being a skew group ring (that is, a group ring where group elements commute past the base field by some non-trivial action).  Rings of this type are called "Galois orders" (but were definitely not discovered Galois).

Recent work has turned up some really interesting examples of these called "Coulomb branches" (don't even ask what Coulomb would have thought of these!).  I'll discuss how to think about the representation theory of these algebras, and how they tie together a lot of recent work of mine.

MC 5403

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