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An invitation to combinatorial representation theory and diagrammatic algebras

Faculty Research Seminar

Speaker: Monica Vazirani, UC Davis
Location: 2112 MSB
Start time: Tue, Feb 18 2020, 12:00PM

The first several levels of Young's lattice of partitions can be easily drawn by an elementary school student. Yet it encodes deep information, in particular about the representation theory of the symmetric group. One can view a standard Young tableau as shorthand for a certain walk on this lattice.

The standard Young tableaux of fixed shape index a basis of an irreducible representation of the symmetric group-- in other words, permutations know how to act on these tableaux (in a non-obvious way). As one generalizes the allowed walks or tableaux, one finds different algebras that act. These include: Hecke algebra, affine Hecke algebras, (affine) BMW algebras, double affine Hecke algebras. I'll draw some pictures of these and try to describe how these combinatorial structures help me to understand the algebras.

Lunch will be served.