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A crystal to rigged configuration bijection for nonexceptional affine algebras

Masato Okado·Anne Schilling·Mark Shimozono
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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.

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Masato Okado, Anne Schilling, Mark Shimozono. 2002-03-16. A crystal to rigged configuration bijection for nonexceptional affine algebras. https://arxiv.org/abs/math/0203163

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