A crystal to rigged configuration bijection for nonexceptional affine algebras

Details A crystal to rigged configuration bijection for nonexceptional affine algebras A crystal to rigged configuration bijection for nonexceptional affine algebras

2002-03-16

arxiv.org/abs/math/0203163v1

"Algebraic Combinatorics and Quantum Groups", Edited by N. Jing, World Scientific (2003), 85-124

Mathematics

Quantum Algebra

34 pages; axodraw.sty file required

Scientific paper

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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