126,297 research outputs found

    RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals

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    We give a new combinatorial model of the Kirillov-Reshetikhin crystals of type An(1)A_n^{(1)} in terms of non-negative integral matrices based on the classical RSK algorithm, which has a simple description of the affine crystal structure without using a promotion operator. We also have a similar description of the Kirillov-Reshetikhin crystals associated to exceptional nodes in the Dynkin diagrams of classical affine or non-exceptional type.Comment: 25 page

    A universal bound on the variations of bounded convex functions

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    Given a convex set CC in a real vector space EE and two points x,yCx,y\in C, we investivate which are the possible values for the variation f(y)f(x)f(y)-f(x), where f:C[m,M]f:C\longrightarrow [m,M] is a bounded convex function. We then rewrite the bounds in terms of the Funk weak metric, which will imply that a bounded convex function is Lipschitz-continuous with respect to the Thompson and Hilbert metrics. The bounds are also proved to be optimal. We also exhibit the maximal subdifferential of a bounded convex function at a given point xCx\in C