Generalized Kostka Polynomials
Page last updated: 5 September 2005
The goal of this web page is to serve as a starting point for
new researchers interested in the subject of Kostka polynomials and
their generalizations. This page contains notes for introductory
lectures on different aspects of Kostka polynomials, an annotated
bibliography of relevant papers from the mathematical literature,
a list of conjectures and open problems, and information about
some useful computer algebra software.
- Loehr 1:
Introduction to Macdonald Polynomials
- Loehr 2:
Quick Definition of Macdonald Polynomials
Lascoux-Leclerc-Thibon (LLT) Polynomials
Macdonald Polynomials and the Geometry of Hilbert Schemes
Kostka Polynomials and Fusion Products
Kostka-Foulkes Polynomials in Other Root Systems
LLT Polynomials, Ribbon Tableaux, and the Affine Quantum Lie Algebra
- Shimozono 1:
Generalized Kostka Polynomials as Parabolic Lusztig $q$-analogues
- Shimozono 2:
One-dimensional Sums for the Impatient
- Shimozono 3:
Crystals for DUMMIES
Papers are grouped by subject. Some papers may
appear under more than one heading.
Generalized Kostka polynomials
Conjectures and Open Problems
Schur Positivity Conjectures
Problems related to Macdonald Polynomials
[from first problem session].
Problems related to k-Schur Functions and Representation Theory
[from second problem session].
Problems related to Fusion Products [from third problem session].
Kostka Polynomials and Root Partition Functions
Generalized Quasisymmetric Invariants
Computer Algebra Packages, Tables, etc.
Installing ACE (Algebraic Combinatorics Environment for Maple) in unix .
posets, coxeter, and weyl (John Stembridge's Maple packages
for symmetric functions, posets, root systems, and finite Coxeter groups).
Maple code for computing generalized Kostka polynomials
Mupad programs for computing generalized Kostka polynomials
Tables of q,t-Kostka polynomials
Information on a 'Q-function' analogue of Kostka polynomials
Mathematica code for computing generalized Kostka polynomials
Documentation for MuPAD-Combinat