Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case

Details Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case

2006-01-28

arxiv.org/abs/math/0601697v2

J.Algebr.Comb.27:55-98,2008

Mathematics

Quantum Algebra

45 pages, version for publication. Introduction revised, more explanations added to the main text

Scientific paper

10.1007/s10801-007-0075-2

In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this paper, we give a proof of crystal theoretic reformulation of the KKR bijection. It is the main claim of Part I (math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the author. The proof is given by introducing a structure of affine combinatorial $R$ matrices on rigged configurations.

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