What is Kazhdan-Lusztig Theory? - Part II

Madeline Nurcombe (The University of Queensland)

05-Nov-2021, 01:00-03:00 (2 years ago)

Abstract: This is Part II of the talk started on 22 October.

In 1979, Kazhdan and Lusztig introduced a new basis for the Hecke algebra of a Coxeter group, related to the standard basis by polynomial coefficients. These polynomials relate diverse areas in Lie Theory, such as Verma modules of semisimple Lie algebras, Schubert varieties in algebraic geometry, and primitive ideals of enveloping algebras, leading to a new topic called Kazhdan-Lusztig theory. In this talk, I will focus on the Kazhdan-Lusztig basis in the simpler case of the Hecke algebra of the symmetric group, giving some necessary background information on the symmetric group, Bruhat order and Hecke algebra. I will then relate this to the more general case of the Hecke algebra of a Coxeter group.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners


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