论文信息 - A CRYSTAL TO RIGGED CONFIGURATION BIJECTION FOR NONEXCEPTIONAL AFFINE ALGEBRAS

A CRYSTAL TO RIGGED CONFIGURATION BIJECTION FOR NONEXCEPTIONAL AFFINE ALGEBRAS

Author(s): Okado, Masato; Schilling, Anne; Shimozono, Mark | Abstract: Kerov, Kirillov, and Reshetikhin defined a bijection between highest weight vectors in the crystal graph of a tensor power of the vector representation, and combinatorial objects called rigged configurations, for type $A^{(1)}_n$. We define an analogous bijection for all nonexceptional affine types, thereby proving (in this special case) the fermionic formulas conjectured by Hatayama, Kuniba, Takagi, Tsuboi, Yamada, and the first author.

Anne Schilling | Mark Shimozono | Masato Okado

[1] I. Stewart,et al. Infinite-dimensional Lie algebras , 1974 .

[2] A. Kirillov,et al. A Generalization of the Kostka–Foulkes Polynomials , 1998, math/9803062.

[3] N. Reshetikhin,et al. Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras , 1990 .

[4] Anatol N. Kirillov,et al. Combinatorics, Bethe Ansatz, and representations of the symmetric group , 1988 .

[5] Masato Okado,et al. Remarks on Fermionic Formula , 1998, math/9812022.

[6] T. Miwa,et al. AFFINE CRYSTALS AND VERTEX MODELS , 1992 .

[7] T. Miwa,et al. Perfect crystals of quantum affine Lie algebras , 1992 .

[8] Anne Schilling,et al. A bijection between Littlewood-Richardson tableaux and rigged configurations , 1999, math/9901037.

[9] Anatol N. Kirillov,et al. The Bethe Ansatz and the combinatorics of Young tableaux , 1988 .