Gaiotto's Lagrangian subvarieties via loop groups
Abstract
The purpose of this note is to give a simple proof of the fact that a certain substack, defined in [2], of the moduli stack $T^{\ast}Bun_G(\Sigma)$ of Higgs bundles over a curve $\Sigma$, for a connected, simply connected semisimple group $G$, possesses a Lagrangian structure. The substack, roughly speaking, consists of images under the moment map of global sections of principal $G$-bundles over $\Sigma$ twisted by a smooth symplectic variety with a Hamiltonian $G$-action.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2017
- arXiv:
- arXiv:1705.01639
- Bibcode:
- 2017arXiv170501639L
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematical Physics;
- Mathematics - Representation Theory