Crystal structure on rigged configurations
arXiv:math/0508107 · doi:10.1155/IMRN/2006/97376
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.
20 pages, 1 figure, axodraw and youngtab style file necessary