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Lecture 2 : The Kostant-Hitchin sections and their Hamiltonian flow

Le : 26/09/2014 11h00
Par : Peter Dalakov (Academie des Sciences, Sophia, Boulgarie)
Lieu : I 001
Lien web :
Résumé : Let G be a simple complex Lie group. The moduli space of semi-stable G-Higgs bundles on a smooth algebraic curve is an algebraic completely integrable Hamiltonian system. One of its connected components admits a (family of) sections, as shown by Hitchin. We review the construction of the Hitchin section and the appropriate Lie-theoretic tools (due to Kostant). We next describe the Hamiltonian flow of the section under linear hamiltonian functions on the Hitchin base. If time permits, we indicate a relation to the question of identifying the Higgs bundles corresponding to G-opers under the non-abelian Hodge theorem.