Crystal structure on rigged configurations

Details Crystal structure on rigged configurations Crystal structure on rigged configurations

2005-08-05

arxiv.org/abs/math/0508107v1

International Mathematics Research Notices, Volume 2006, Article ID 97376, Pages 1-27

Mathematics

Quantum Algebra

20 pages, 1 figure, axodraw and youngtab style file necessary

Scientific paper

10.1155/IMRN/2006/97376

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.

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