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Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection

Atsuo Kuniba·Masato Okado·Reiho Sakamoto·Taichiro Takagi·Yasuhiko Yamada
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Abstract

The Kerov-Kirillov-Reshetikhin (KKR) bijection is the crux in proving fermionic formulas. It is defined by a combinatorial algorithm on rigged configurations and highest paths. We reformulate the KKR bijection as a vertex operator by purely using combinatorial R in crystal base theory. The result is viewed as a nested Bethe ansatz at q=0 as well as the direct and the inverse scattering (Gel'fand-Levitan) map in the associated soliton cellular automaton.

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Atsuo Kuniba, Masato Okado, Reiho Sakamoto, Taichiro Takagi, Yasuhiko Yamada. 2006-01-26. Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection. https://doi.org/10.1016/j.nuclphysb.2006.02.005

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