Introduction to the Hecke category and the diagonalization of the full twist
Ben Elias (Univ. Oregon)
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 topologycategory theoryquantum algebra
Audience: researchers in the topic
( video )
Topological Quantum Field Theory Club (IST, Lisbon)
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