SLn webs first emerged in invariant theory and have a recent reformulation by Cautis-Kamnitzer-Morrison (2014). A collection of these webs form a basis of the Specht modules for the symmetric groups. On the other hand, classical construction of the Specht modules uses the polytabloids basis parameterized by standard Young tableaux. Russell-Tymoczko (2020) showed that the transitioning matrix from the polytabloid basis to the web basis is unitriangular. We further proved their conjecture that the upper-triangular entries are positive. The talk will be mostly focused on SL2 webs, with some preliminary results on SL3 webs. This is joint work with M. S. Im.
This video is part of the University of Georgia‘s Algebra seminar.
