Higgs bundles on weighted projective lines and loop crystals
Representation Theory
2015-06-30 v2
Abstract
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.
Cite
@article{arxiv.1312.5838,
title = {Higgs bundles on weighted projective lines and loop crystals},
author = {Guillaume Pouchin},
journal= {arXiv preprint arXiv:1312.5838},
year = {2015}
}
Comments
Contains generalizations of some results of arXiv:1005.3732