Mathematics Colloquia and Seminars

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To learn about the representation theory of quantum SL(2), one can study the Temperley-Lieb category, whose basis morphisms are planar matchings. A generalization to the SL(3) case gives rise to the SL(3) web category, whose basis morphisms are known as non-elliptic webs - planar trivalent graphs with girth greater or equal to 6.     It is shown by Fontaine-Kamnitzer-Kuperberg that the dual graphs of basis webs are embedded isometrically into the affine building, defined as a simplicial complex with vertices given by the affine grassmannian. I will talk about generalizations to the SL(4) case. Based on upcoming joint work with Gaetz-Striker-Swanson.