Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 079, 14 pages      arXiv:2009.13573      https://doi.org/10.3842/SIGMA.2021.079

Triality for Homogeneous Polynomials

Laura P. Schaposnik ^a and Sebastian Schulz ^b
a) University of Illinois at Chicago, USA
^b) University of Texas at Austin, USA

Received February 15, 2021, in final form August 18, 2021; Published online August 27, 2021

Abstract
Through the triality of ${\rm SO}(8,\mathbb{C})$, 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.

Key words: triality; Higgs bundles; invariant polynomials.

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