Introduction to the Hecke category and the diagonalization of the full twist

Abstract: The group algebra of the symmetric group has a large commutative subalgebra generated by Young-Jucys-Murphy elements, which acts diagonalizably on any irreducible representation. The goal of this talk is to give an accessible introduction to the categorification of this story. The main players are: Soergel bimodules, which categorify the Hecke algebra of the symmetric group; Rouquier complexes, which categorify the braid group where Young-Jucys-Murphy elements live; and the Elias-Hogancamp theory of categorical diagonalization, which allows one to construct projections to "eigencategories."

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar