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.
Lecture Notes
 Loehr 1:
Introduction to Macdonald Polynomials
 Loehr 2:
Quick Definition of Macdonald Polynomials
 Lam:
LascouxLeclercThibon (LLT) Polynomials
 Haiman:
Macdonald Polynomials and the Geometry of Hilbert Schemes
 Zabrocki:
Creation Operators
 Morse:
kSchur Functions
 Kedem:
Kostka Polynomials and Fusion Products
 Schwer:
Galleries
 Stembridge:
KostkaFoulkes Polynomials in Other Root Systems
 Descouens:
LLT Polynomials, Ribbon Tableaux, and the Affine Quantum Lie Algebra
 Shimozono 1:
Generalized Kostka Polynomials as Parabolic Lusztig $q$analogues
 Shimozono 2:
Onedimensional Sums for the Impatient
 Shimozono 3:
Crystals for DUMMIES
Annotated Bibliography
Papers are grouped by subject. Some papers may
appear under more than one heading.

Background

Macdonald polynomials

Generalized Kostka polynomials
Conjectures and Open Problems

Schur Positivity Conjectures

K=LLT Conjecture

Problems related to Macdonald Polynomials
[from first problem session].

Problems related to kSchur 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 .
 SF,
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,tKostka polynomials

Information on a 'Qfunction' analogue of Kostka polynomials

Mathematica code for computing generalized Kostka polynomials

Documentation for MuPADCombinat