New fermionic formula for unrestricted Kostka polynomials
Combinatorics
2013-12-19 v2 Quantum Algebra
Abstract
A new fermionic formula for the unrestricted Kostka polynomials of type is presented. This formula is different from the one given by Hatayama et al. and is valid for all crystal paths based on Kirillov-Reshetihkin modules, not just for the symmetric and anti-symmetric case. The fermionic formula can be interpreted in terms of a new set of unrestricted rigged configurations. For the proof a statistics preserving bijection from this new set of unrestricted rigged configurations to the set of unrestricted crystal paths is given which generalizes a bijection of Kirillov and Reshetikhin.
Keywords
Cite
@article{arxiv.math/0509194,
title = {New fermionic formula for unrestricted Kostka polynomials},
author = {Lipika Deka and Anne Schilling},
journal= {arXiv preprint arXiv:math/0509194},
year = {2013}
}
Comments
35 pages; reference added