Speaker: Justin Davis
Abstract: Combinatorics is an interesting topic on its own, but is also a very useful tool throughout mathematics. Due to the nature of the subject, combinatorics is extremely prevalent in representation theory, whether it's classifying all finite dimensional irreducible representations, or decomposing representations into irreducible pieces. I will discuss a combinatorial rule, originally called the "Littlewood-Richardson Rule" for decomposing tensor products of two irreducible representations for the Lie algebra sln+1. This uses some interesting combinatorics of partitions of natural numbers. Lastly, I will discuss how I am using this rule to find the decomposition into irreducible representations of certain representations of sln+1 coming from a family of prime representations of quantum affine sln+1 recently defined by Brito and Chari.
Friday, March 9 at 1:10pm to 2:00pm
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