Летняя математическая школа "Алгебра и геометрия"

Алгебры Гекке и их представления

Давид Каждан (Hebrew University of Jerusalem, Израиль; Harvard University, США)

Видеозаписи лекций

• Лекция 1
• Лекция 2

Резюме

Abstract. I'll define KL-polynomials, explain the relevance for different questions in the representation theory, explain the Soergel's categorification and possibly will discuss the recent proof of the positivity conjecture by Ben Elias and Geordie Williamson.

Some useful materials:

• First 2-3 sections of the Soergel's article "Kazhdan-Lusztig Polynomials and a Combinatoric for Tilting Modules"
• First 5 sections of the Soergel's article "Kazhdan-Lusztig-polynomials and indecomposable bimodules over polynomial rings"
• The introduction from arXiv:1212.0791 "The Hodge theory of Soergel bimodules"