Triality for Homogeneous Polynomials

Abstract

Through the triality of $\mathrm{SO}(8,\mathbb{C})$, we study three interrelated homogeneous basis of the ring of invariant polynomials of Lie algebras, which give the basis of three Hitchin fibrations, and identify the explicit automorphisms that relate them.

References in corpus (7)

• Mirror symmetry, Langlands duality, and the Hitchin system
• From Dynkin diagram symmetries to fixed point structures
• Exceptional Lie groups
• Spectral data for G-Higgs bundles
• Branes through finite group actions
• Le lemme fondamental pour les algebres de Lie
• Higgs bundles -- Recent applications