Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
Abstract
Description
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.
45 pages, version for publication. Introduction revised, more explanations added to the main text
45 pages, version for publication. Introduction revised, more explanations added to the main text