A CRYSTAL TO RIGGED CONFIGURATION BIJECTION FOR NONEXCEPTIONAL AFFINE ALGEBRAS

By M. Okado, Anne Schilling, Mark Shimozono. 2002

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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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2da0c433a0703664d1cbae486566c6bd5278844f