Cayley and Langlands type correspondences for orthogonal Higgs bundles

Abstract

Through Cayley and Langlands type correspondences, we give a geometric description of the moduli spaces of real orthogonal and symplectic Higgs bundles of any signature in the regular fibres of the Hitchin fibration. As applications of our methods, we complete the concrete abelianization of real slices corresponding to all quasi-split real forms, and describe how extra components emerge naturally from the spectral data point of view.

34 pages, comments welcomed!

References in corpus (2)

• Spectral data for G-Higgs bundles
• Cameral data for SU(p+1,p)-Higgs bundles

Cited by in corpus (10)

• Singular Geometry and Higgs Bundles in String Theory
• Unramified covers and branes on the Hitchin system
• SO(p,q)-Higgs bundles and higher Teichmüller components
• Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups
• Exotic components of $\mathrm{SO}(p,q)$ surface group representations, and their Higgs bundle avatars
• Mirror symmetry for Nahm branes
• A general Cayley correspondence and higher Teichmüller spaces
• Orthogonal Higgs bundles with singular spectral curves
• Studying Deformations of Fuchsian Representations with Higgs Bundles
• Topological invariants of parabolic $G$-Higgs bundles