2023/06/21 by Christian Gaetz, Gaetz, Christian, Oliver Pechenik +7 · 9 citations
Mathematics · Chemistry · Biochemistry, Genetics and Molecular Biology · #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2306.12501
Webs give a diagrammatic calculus for spaces of tensor invariants. We introduce hourglass plabic graphs as a new avatar of webs, and use these to give the first rotation-invariant Uq(\mathfraksl4)-web basis, a long-sought object. The characterization of our basis webs relies on the combinatorics of these new plabic graphs and associated configurations of a symmetrized six-vertex model. We give growth rules, based on a novel crystal-theoretic technique, for generating our basis webs from tableaux and we use skein relations to give an algorithm for expressing arbitrary webs in the basis. We also discuss how previously known rotation-invariant web bases can be unified in our framework of hourglass plabic graphs.