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Combinatorics of two-boundary Temperley-Lieb algebras

Zajj Daugherty, Reed College
Wednesday, May 31, 2023 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:


The two boundary Temperley-Lieb algebra arises originally in the transfer matrix formulation of lattice models in Statistical Mechanics, via the introduction of integrable boundary terms to the six-vertex model. Algebraically, it is presented as a diagram algebra consisting of certain planar diagrams similar to classic Temperley-Lieb diagrams; as a quotient of a two-pole braid group algebra; and as a quotient of a type C affine Hecke algebra. It also has a natural action on tensor space giving a Schur-Weyl duality with the quantum group \$U_q gl_2\$. This all comes together to provide many combinatorial ways of encoding the representations of this beautiful algebra, which we will explore in this talk.


Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974