Algebraic Geometry and Combinatorics Seminar: Stranding sl_n webs

Abstract: Webs are graphs that provide combinatorial models in the representation theory of quantum sl_n, with important connections to quantum knot invariants. In the low-rank sl_2 and sl_3 cases, the graphical relations on webs naturally determine reduced web bases with many remarkable properties. The story for sl_4 and beyond is much less clear. In this talk, I will describe strandings, a global combinatorial structure on sl_n webs motivated by recapturing the combinatorics available in the low-rank setting. Strandings give an explicit way to compute the vector associated to a web as a weighted sum over all strandings the web supports. I will focus on the motivation for this construction, use small-rank examples to illustrate how the combinatorics changes in higher rank, and discuss connections with tableaux and web bases.

Host: Martha Precup