Seminar

The study of solvable lattice models originated in statistical mechanics, and has since formed rich connections with areas of math including combinatorics, probability, and representation theory. Lattice models are called solvable when they can be studied using the Yang-Baxter equation. The partition function of a system, which captures global information about the lattice model, is at the heart of many of these connections with other areas. To compute the partition function, one method is to identify boundary conditions that give systems with a unique state, from which other systems can be computed by Demazure recursion relations coming from the Yang-Baxter equation. Bosonic and colored variants of solvable lattice models have been studied in recent years by Aggarwal, Borodin, Brubaker, Buciumas, Bump, Gustafsson, Naprienko, Wheeler, and others. We will define a class of these models which are bosonic and include two types of colors, generalizing the now widely-studied colored models. These bicolored bosonic models satisfy the Yang-Baxter equation, which gives a four-term recurrence relation on the partition function. We will give conditions on the number of states of the model based on boundary conditions in terms of the Bruhat order, and discuss connections with Gelfand-Tsetlin patterns.