Combinatorics and representation theory of Temperley-Lieb algebras (Zajj Daugherty, CUNY)

The classical, one-boundary, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as “diagram algebras”, meaning that they have basis elements depicted as certain kinds of graphs, and multiplication rules are given by stacking diagrams and gluing of vertices. In this talk, we will explore these algebras and their representation theory, as well as their relationship to other important diagram algebras in combinatorial representation theory.