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We consider the space of nilpotent Higgs bundles on a weighted projective line, as a global analog of the nilpotent cone. We show that it is pure, compute its dimension, and define geometric correspondences between irreducible components. We prove it by constructing a loop analog of a cristal, in the spirit of Kashiwara and Saito, for some corresponding loop Kac-Moody algebra.
|Publication status||Published - 20 Dec 2013|
- 14H60, 05E10
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- 1 Finished
1/09/11 → 31/08/14