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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 079, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.079 (Mi sigma1761) 		 
Triality for Homogeneous Polynomials

Laura P. Schaposnika, Sebastian Schulzb

a University of Illinois at Chicago, USA
b University of Texas at Austin, USA
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DOI: https://doi.org/10.3842/SIGMA.2021.079
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.
Keywords: triality, Higgs bundles, invariant polynomials.
Funding agency Grant number
National Science Foundation 1107452
1107263
1107367
1509693
1749013
1440140
The work of S.S. is partially supported by NSF grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties (the GEAR Network)”. L.P.S. was partially supported by NSF DMS 1509693 and NSF CAREER Award DMS 1749013, as well as by the Alexander Von Humboldt foundation. This material is also based upon work supported by NSF DMS 1440140 while L.P.S. was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2019 semester.
Received: February 15, 2021; in final form August 18, 2021; Published online August 27, 2021
Bibliographic databases:
Document Type: Article
MSC: 14H60, 31A35, 33C80, 53C07
Language: English
Citation: Laura P. Schaposnik, Sebastian Schulz, “Triality for Homogeneous Polynomials”, SIGMA, 17 (2021), 079, 14 pp.
Citation in format AMSBIB
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