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International Mathematics Research Notices (2006) Vol. 2006 : article ID 97376, 27 pages, doi:10.1155/IMRN/2006/97376
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Crystal structure on rigged configurations

Anne Schilling

Department of Mathematics, University of California Davis, One Shields Avenue, Davis, CA 95616-8633, USA E-mail address: anne{at}math.ucdavis.edu

Rigged configurations are combinatorial objects originating from the Bethe ansatz, which 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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