Generalized Kostka Polynomials
July 18 to July 22, 2005
American Institute of Mathematics,
Palo Alto, California
Anne Schilling and Monica Vazirani
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.
- 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.
Computer Algebra Packages, Tables, etc.
Generalized Kostka polynomials
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
The workshop schedule.
A report on the workshop activities.
A list of open problems.