Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 028, 88 pages      arXiv:1302.4562
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

Rigged Configurations and Kashiwara Operators

Reiho Sakamoto
Department of Physics, Tokyo University of Science, Kagurazaka, Shinjuku, Tokyo, Japan

Received April 02, 2013, in final form February 28, 2014; Published online March 23, 2014

For types $A^{(1)}_n$ and $D^{(1)}_n$ we prove that the rigged configuration bijection intertwines the classical Kashiwara operators on tensor products of the arbitrary Kirillov-Reshetikhin crystals and the set of the rigged configurations.

Key words: crystal bases; rigged configurations; quantum affine algebras; box-ball systems.

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