Finding Rigged Configurations From Paths
نویسنده
چکیده
in terms of the crystal bases theory [K] and its application to the periodic box-ball systems following [S2] and [KS3]. The bijection φ was originally introduced in order to show the so-called X = M formula (see [O, S4] for reviews) by using its statistic preserving property. Recently, another application of the bijection φ to the box-ball systems [TS, T] was found [KOSTY]. In this context, the bijection φ plays the role of the inverse scattering formalism [GGKM, AC] for the box-ball systems. The original definition of the bijection φ is described by purely combinatorial language such as box adding or removing procedures. Purpose of this note is to clarify what the representation theoretic origin of the bijection φ is. Motivated by the connection with the box-ball systems, consider the following isomorphism under the affine combinatorial R:
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