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We consider the space of nilpotent Higgs bundles on a weighted projectiveline, as a global analog of the nilpotent cone. We show that it is pure,compute its dimension, and define geometric correspondences between irreduciblecomponents. We prove it by constructing a loop analog of a cristal, in thespirit of Kashiwara and Saito, for some corresponding loop Kac-Moody algebra.

Higgs bundles on weighted projective lines and loop crystals