Generalized Kostka Polynomials

July 18 to July 22, 2005

at the

American Institute of Mathematics, Palo Alto, California

organized by

Anne Schilling and Monica Vazirani

Original Announcement

This workshop concerns Kostka polynomials and their connections to various areas of mathematics. Kostka polynomials and their generalizations have arisen in numerous ways such as in the context of symmetric functions, combinatorics, representation theory, quantum groups and crystal bases, statistical mechanics, algebraic geometry, and Kazhdan-Lusztig theory. The goal of this workshop is to bring together mathematicians who have studied Kostka polynomials from different points of views, state the various connections and open conjectures, and work towards their proofs.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Lecture Notes:

  1. Loehr 1: Introduction to Macdonald Polynomials
  2. Loehr 2: Quick Definition of Macdonald Polynomials
  3. Lam: Lascoux-Leclerc-Thibon (LLT) Polynomials
  4. Haiman: Macdonald Polynomials and the Geometry of Hilbert Schemes
  5. Zabrocki: Creation Operators
  6. Morse: k-Schur Functions
  7. Kedem: Kostka Polynomials and Fusion Products
  8. Schwer: Galleries
  9. Stembridge: Kostka-Foulkes Polynomials in Other Root Systems
  10. Descouens: LLT Polynomials, Ribbon Tableaux, and the Affine Quantum Lie Algebra
  11. Shimozono 1: Generalized Kostka Polynomials as Parabolic Lusztig $q$-analogues
  12. Shimozono 2: One-dimensional Sums for the Impatient
  13. Shimozono 3: Crystals for DUMMIES
Annotated Bibliography:
Papers are grouped by subject. Some papers may appear under more than one heading.
  1. Background
  2. Macdonald polynomials
  3. Generalized Kostka polynomials
Computer Algebra Packages, Tables, etc.
  1. Installing ACE (Algebraic Combinatorics Environment for Maple) in unix .
  2. SF, posets, coxeter, and weyl (John Stembridge's Maple packages for symmetric functions, posets, root systems, and finite Coxeter groups).
  3. Maple code for computing generalized Kostka polynomials
  4. Mupad programs for computing generalized Kostka polynomials
  5. Tables of q,t-Kostka polynomials
  6. Information on a 'Q-function' analogue of Kostka polynomials
  7. Mathematica code for computing generalized Kostka polynomials
  8. Documentation for MuPAD-Combinat