Crystal structure on rigged configurations
Quantum Algebra
2007-10-08 v1 Combinatorics
Abstract
Rigged configurations are combinatorial objects originating from the Bethe Ansatz, that label highest weight crystal elements. In this paper a new unrestricted set of rigged configurations is introduced for types ADE by constructing a crystal structure on the set of rigged configurations. In type A an explicit characterization of unrestricted rigged configurations is provided which leads to a new fermionic formula for unrestricted Kostka polynomials or q-supernomial coefficients. The affine crystal structure for type A is obtained as well.
Keywords
Cite
@article{arxiv.math/0508107,
title = {Crystal structure on rigged configurations},
author = {Anne Schilling},
journal= {arXiv preprint arXiv:math/0508107},
year = {2007}
}
Comments
20 pages, 1 figure, axodraw and youngtab style file necessary