152 research outputs found

    Epsilon Systems on Geometric Crystals of Type AnA_n

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    We introduce an epsilon system on a geometric crystal of type AnA_n, which is a certain set of rational functions with some nice properties. We shall show that it is equipped with a product structure and that it is invariant under the action of tropical R maps

    Geometric Crystals on Unipotent Groups and Generalized Young Tableaux

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    We define geometric/unipotent crystal structure on unipotent subgroups of semi-simple algebraic groups. We shall show that in AnA_n-case, their ultra-discretizations coincide with crystals obtained by generalizing Young tableaux.Comment: LaTeX 17 page