Speaker: Ashleigh Adams (Fargo ND)
Title: Webification of Symmetry Classes of Plane Partitions via Webs
Abstract:
Plane partitions are a combinatorial object generalizing Young diagrams. They have beautiful combinatorial properties, such as product counting formulas for their symmetry classes. Recently, plane partitions have been shown by Gaetz, Pechenik, Pfannerer, Striker, and Swanson to be in bijection with certain \(U_q(sl_4)\)-webs lying on a hexagonal grid. \(U_q(sl_4)\)-webs can be viewed as combinatorial objects called hourglass plabic graphs and have deep representation theoretic connections to quantum invariant theory. In this talk, we discuss the connection between these seemingly very unrelated combinatorial objects. Moreover, we classify the symmetry classes of plane partitions via lattice words obtained from analyzing trip permutations of the corresponding hourglass plabic graphs, as well as some representation theoretic implications.