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Kostka polynomials and energy functions in solvable lattice models

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Abstract.

The relation between the charge of Lascoux-Schützenberger and the energy function in solvable lattice models is clarified. As an application, A.N. Kirillov's conjecture on the expression of the branching coefficient of \({\widehat{{\frak {sl}}_n}}/{\frak {sl}}_n\) of Kostka polynomials is proved.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Ropponmatsu 4-2-1, Fukuoka 810, Japan, e-mail: atsushi@rc.kyushu-u.ac.jp, , , , , , JP

    A. Nakayashiki

  2. Department of Mathematics, Faculty of Science, Kobe University, Kobe, Japan, e-mail: yamaday@math.s.kobe-u.ac.jp, , , , , , JP

    Y. Yamada

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  1. A. Nakayashiki
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  2. Y. Yamada
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Nakayashiki, A., Yamada, Y. Kostka polynomials and energy functions in solvable lattice models. Sel. math., New ser. 3, 547–599 (1997). https://doi.org/10.1007/s000290050020

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  • DOI: https://doi.org/10.1007/s000290050020

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