Clare Minnerath, University of Washington
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PDL C-38
The study of \$SL_r(\mathbb{C})\$ tensor invariants has been extended by the addition of tensor diagrams. The search for a basis among webs, the planar version of tensor diagrams, has yielded compelling results for \$r=2\$ and \$3\$, but has proven elusive for larger \$r\$. In an example forward fashion, we will see how you can go from a tensor diagram to an element of the invariant ring, explore the known web bases for \$SL_2\$ and \$SL_3\$ invariants, and discuss what properties we hope for in a web basis when \$r\ge 4\$.
Based on lectures given by Christian Gaetz at SLMath: Graphical Models in Algebraic Combinatorics.