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

Abstract

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

References in corpus (6)

• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• X=M for symmetric powers
• Tau functions in combinatorial Bethe ansatz
• New fermionic formula for unrestricted Kostka polynomials
• Crystal structure on rigged configurations
• Rigged configurations and the Bethe Ansatz

Cited by in corpus (14)

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• Tau functions in combinatorial Bethe ansatz
• Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations
• Affine crystal structure on rigged configurations of type D_n^(1)
• Kirillov--Schilling--Shimozono bijection as energy functions of crystals
• Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations
• Box-Basket-Ball Systems
• Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types
• Ultradiscrete Soliton Systems and Combinatorial Representation Theory
• A uniform approach to soliton cellular automata using rigged configurations
• Finding Rigged Configurations From Paths
• Paths and Kostka--Macdonald Polynomials
• Promotion operator on rigged configurations of type A
• A crystal theoretic method for finding rigged configurations from paths