Topics on Combinatorics 8680: Kazhdan-Lusztig Theory

Office hours: MWF 2-3pm, Vincent 258

Time and Place: M,W,F 11:15 AM - 12:05 PM, Vincent Hall 301

The class will cover elementary aspects of Kazhdan-Lusztig theory, concentrating on type A and affine type A. It will also cover applications to combinatorics, i.e. relations to total positivity, symmetric functions, etc. Grading will be based on homeworks and paper presentation.

Textbook: Combinatorics of Coxeter Groups by Bjorner and Brenti, available online.

Recommended book: Reflection Groups and Coxeter Groups by Humphreys, available online.

Some other papers that may be covered during the class:

Hecke algebra characters and immanant conjectures by Haiman.

Kazhdan–Lusztig immanants and products of matrix minors by Rhoades and Skandera.

Kazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations by Billey and Warrington.

Matrix-Ball Construction of affine Robinson-Schensted correspondence by Chmutov, Pylyavskyy, Yudovina.

Monodromy in Kazhdan-Lusztig cells in affine type A by Chmutov, Lewis, Pylyavskyy.

Admissible W-graphs by Stembridge. Admissible W-graphs by Stembridge.

Admissible W-graphs and commuting Cartan matrices by Stembridge.

The structure of W-graphs arising in Kazhdan-Lusztig theory by Chmutov.

Proof of a conjecture on immanants of the Jacobi-Trudi matrix by Greene.

Quasisymmetric functions and Kazhdan-Lusztig polynomials by Billera and Brenti.

Special matchings and Kazhdan-Lusztig polynomials by Brenti.

Diamonds and Hecke algebra representations by Brenti.

The Kazhdan–Lusztig polynomial of a matroid by Elias, Proudfoot, Wakefield.

A Generalization of Deodhar's Framework for Questions in Kazhdan-Lusztig Theory by Agrawal, Sotirov.

Type A Molecules are Kazhdan-Lusztig by Chmutov.

Type A-admissible cells are Kazhdan–Lusztig by Nguyen.