Higgs bundles for real groups and the Hitchin-Kostant-Rallis section

@article{GarcaPrada2015HiggsBF,
  title={Higgs bundles for real groups and the Hitchin-Kostant-Rallis section},
  author={Oscar Garc{\'i}a-Prada and Ana Pe'on-Nieto and S.Ramanan},
  journal={arXiv: Algebraic Geometry},
  year={2015},
  pages={2907-2953}
}
  • Oscar García-Prada, Ana Pe'on-Nieto, S.Ramanan
  • Published 2015
  • Mathematics
  • arXiv: Algebraic Geometry
  • We consider the moduli space of polystable $L$-twisted $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a real reductive Lie group, and $L$ is a holomorphic line bundle over $X$. Evaluating the Higgs field at a basis of the ring of polynomial invariants of the isotropy representation, one defines the Hitchin map. This is a map to an affine space, whose dimension is determined by $L$ and the degrees of the polynomials in the basis. Building up on the work of Kostant-Rallis and… CONTINUE READING

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