New fermionic formula for unrestricted Kostka polynomials

Details New fermionic formula for unrestricted Kostka polynomials New fermionic formula for unrestricted Kostka polynomials

2005-09-08

arxiv.org/abs/math/0509194v1

J. Combinatorial Theory, Series A 113 (2006) 1435-1461

Mathematics

Combinatorics

35 pages

Scientific paper

10.1016/j.jcta.2006.01.003

A new fermionic formula for the unrestricted Kostka polynomials of type A_{n-1}^{(1)} 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.

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