MAGIC115: Lusztig’s conjecture

The course covers the basics of Hecke categories and their associated p-Kazhdan–Lusztig polynomials. Over the past decade, Hecke categories have arisen as some of the most important structures in representation theory and have been used to resolve some of the field’s most famous conjectures. The purpose of this course is to give a hands-on introduction to working with Hecke categories and a thorough grounding in their basic structures.

Familiarity with abstract algebra and complex representation theory or character theory of symmetric groups is desirable. The following are no strict pre-requisites, but familiarity with the ideas discussed in the following books would not hurt:

Chapter 1-11 of James-Liebeck’s book “Representations and characters of groups”.
Chapter 2 of Mathas' book "Iwahori–Hecke algebras and Schur algebras of the symmetric group"
Chapters 5-6 of Bowman's book "Diagrammatic Algebra" (preprint available in the "files" section of this course)

Topics covered:
(1) Cellular algebras
(2) Representations of Schur algebras and symmetric groups
(3) Kazhdan-Lusztig polynomials via Temperley—Lieb combinatorics
(4) General Kazhdan-Lusztig polynomials
(5) The Hecke category of maximal parabolics of symmetric groups
(6) The Hecke category of the affine symmetric group
(7) Intersection forms
(8) Torsion explosion in the Hecke category

MAGIC115: Lusztig’s conjecture

Course details

Semester

Hours

Timetable

Description

Prerequisites

Syllabus

Lecturer

Chris Bowman-Scargill

Bibliography

Assessment

Files

Lectures