Generators and Relations Talk 2

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After a quick recap of last week, I tell you about Gelfand-Tsetlin bases, and how these allow us to lift the forgetful functor from $Rep(U_q(\mathfrak{sl}_n))$ to $Rep(U_q(\mathfrak{sl}_{n-1}))$ up to the level of diagrams. The diagrammatic functor will be easy to calculate using a little combinatorial recipe, with no representation theory involved! I then begin using this to inductively discover new relations, starting at $\mathfrak{sl}_3$ and working up.