Mots-clés : invariant polynomials.
@article{SIGMA_2021_17_a78,
author = {Laura P. Schaposnik and Sebastian Schulz},
title = {Triality for {Homogeneous} {Polynomials}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2021},
volume = {17},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a78/}
}
Laura P. Schaposnik; Sebastian Schulz. Triality for Homogeneous Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a78/
[1] Aganagic M., Haouzi N., Shakirov S., $A_n$-triality, arXiv: 1403.3657
[2] Antón Sancho Á., Fibrados de Higgs y trialidad, Ph.D. Thesis, Universidad Complutense de Madrid, 2009
[3] Baraglia D., Schaposnik L. P., “Real structures on moduli spaces of Higgs bundles”, Adv. Theor. Math. Phys., 20 (2016), 525–551, arXiv: 1309.1195 | DOI
[4] Beck F., Donagi R., Wendland K., “Folding of Hitchin systems and crepant resolutions”, Int. Math. Res. Not. (to appear) , arXiv: 2004.04245 | DOI
[5] Corlette K., “Flat $G$-bundles with canonical metrics”, J. Differential Geom., 28 (1988), 361–382 | DOI
[6] Donagi R., Pantev T., “Langlands duality for Hitchin systems”, Invent. Math., 189 (2012), 653–735, arXiv: math.AG/0604617 | DOI
[7] Donaldson S. K., “Twisted harmonic maps and the self-duality equations”, Proc. London Math. Soc., 55 (1987), 127–131 | DOI
[8] Fuchs J., Schellekens B., Schweigert C., “From Dynkin diagram symmetries to fixed point structures”, Comm. Math. Phys., 180 (1996), 39–97, arXiv: hep-th/9506135 | DOI
[9] García-Prada O., Ramanan S., “Involutions and higher order automorphisms of Higgs bundle moduli spaces”, Proc. Lond. Math. Soc., 119 (2019), 681–732, arXiv: 1605.05143 | DOI
[10] Hausel T., Thaddeus M., “Mirror symmetry, Langlands duality, and the Hitchin system”, Invent. Math., 153 (2003), 197–229, arXiv: math.AG/0205236 | DOI
[11] Heller S., Schaposnik L. P., “Branes through finite group actions”, J. Geom. Phys., 129 (2018), 279–293, arXiv: 1611.00391 | DOI
[12] Hitchin N. J., “The self-duality equations on a Riemann surface”, Proc. London Math. Soc., 55 (1987), 59–126 | DOI
[13] Hitchin N. J., “Stable bundles and integrable systems”, Duke Math. J., 54 (1987), 91–114 | DOI
[14] Hitchin N. J., “Langlands duality and $G_2$ spectral curves”, Q. J. Math., 58 (2007), 319–344, arXiv: math.AG/0611524 | DOI
[15] Kapustin A., Witten E., “Electric-magnetic duality and the geometric Langlands program”, Commun. Number Theory Phys., 1 (2007), 1–236, arXiv: hep-th/0604151 | DOI
[16] Lawson Jr. H.B., Michelsohn M. L., Spin geometry, Princeton Mathematical Series, 38, Princeton University Press, Princeton, NJ, 1989
[17] Ngô B.C., “Le lemme fondamental pour les algèbres de Lie”, Publ. Math. Inst. Hautes Études Sci., 111 (2010), 1–169, arXiv: 0801.0446 | DOI
[18] Schaposnik L. P., Spectral data for $G$-Higgs bundles, Ph.D. Thesis, University of Oxford, 2013, arXiv: 1301.1981
[19] Schaposnik L. P., “Higgs bundles – recent applications”, Notices Amer. Math. Soc., 67 (2020), 625–634, arXiv: 1909.10543 | DOI
[20] Simpson C. T., “Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization”, J. Amer. Math. Soc., 1 (1988), 867–918 | DOI
[21] Slodowy P., Simple singularities and simple algebraic groups, Lecture Notes in Math., 815, Springer, Berlin, 1980 | DOI
[22] Springer T. A., Linear algebraic groups, Modern Birkhäuser Classics, 2nd ed., Birkhäuser Boston, Inc., Boston, MA, 2009 | DOI
[23] Uhlenbeck K., Yau S.-T., “On the existence of Hermitian–Yang–Mills connections in stable vector bundles”, Comm. Pure Appl. Math., 39 (1986), S257–S293 | DOI
[24] Wolf J. A., Gray A., “Homogeneous spaces defined by Lie group automorphisms I”, J. Differential Geometry, 2 (1968), 77–114 | DOI
[25] Yokota I., Exceptional Lie groups, arXiv: 0902.0431