Crystal structure on rigged configurations

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

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Cited by in corpus (12)

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• On the uniqueness of promotion operators on tensor products of type A crystals
• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Type $D_n^{(1)}$ rigged configuration bijection
• On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models
• Rigged configurations and the $\ast$-involution
• Rigged configurations as tropicalizations of loop Schur functions
• Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebras
• Rigged Configuration Descriptions of the Crystals B(infinity) and B(lambda) for Special Linear Lie Algebras
• Virtual Crystals and Nakajima Monomials