Richard P. Stanley Seminar in Combinatorics: An SL(4) web basis from hourglass plabic graphs


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September 20, 2023 4:15 pm - 5:15 pm
Science Center 232

Christian Gaetz - Cornell

The SL(3) web basis is a special basis of certain spaces of tensor invariants developed in the late 90's by Khovanov and Kuperberg as a tool for computing quantum link invariants. Since then this basis has found connections and applications to cluster algebras, canonical bases, dimer models, quantum topology, and tableau combinatorics. A main open problem has remained: how to find a basis replicating the desirable properties of this basis for SL(4) and beyond? I will describe joint work with Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Josh Swanson in which we construct such a basis for SL(4). Modified versions of plabic graphs and the six-vertex model and new tableau combinatorics will appear along the way.


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