Representations and Lie Theory Seminar

Schedule of talks:

Abstracts

September 22, 2026. The six vertex model, a model originating in statistical mechanics, has weights related to the R-matrix of qunatum affine sl(n). When the model has an open boundary, additional weights satisfying the so-called reflection equation are needed, and this is related to the K-matrix of a quantum symmetric space. Fusion is a procedure to obtain more complex weights from simpler ones (or a method of obtaining R-matrices for Verma modules from the standard representation). While the general procedure is understood for a while, for many probablistic and combinatorial applications one requires explicit tractable formulas. These have been found for bulk weights, but not for the boundary ones.
In joint work in progress with Amol Aggarwal, Ivan Corwin, Milinde Hegde, and Michael Wheeler, we extend fusion to boundary weights in a special case known as the boson model. This is already enough for many interesting applications. I will explain the physical background and connections to quantum groups, provide an overview of fusion, and explain some of the possible applications within probability and combinatorics that our work may allow.