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arXiv · 0711.4185

Kirillov--Schilling--Shimozono bijection as energy functions of crystals

Reiho Sakamoto
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Abstract

The Kirillov--Schilling--Shimozono (KSS) bijection appearing in theory of the Fermionic formula gives an one to one correspondence between the set of elements of tensor products of the Kirillov--Reshetikhin crystals (called paths) and the set of rigged configurations. It is a generalization of Kerov--Kirillov--Reshetikhin bijection and plays inverse scattering formalism for the box-ball systems. In this paper, we give an algebraic reformulation of the KSS map from the paths to rigged configurations, using the combinatorial R and energy functions of crystals. It gives a characterization of the KSS bijection as an intrinsic property of tensor products of crystals.

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Reiho Sakamoto. 2008-10-30. Kirillov--Schilling--Shimozono bijection as energy functions of crystals. https://doi.org/10.1093/imrn%2Frnn140

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