Triality for Homogeneous Polynomials
Through the triality of SO(8, ℂ), we study three interrelated homogeneous bases of the ring of invariant polynomials of Lie algebras, which give the bases of three Hitchin fibrations, and identify the explicit automorphisms that relate them.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211344 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Triality for Homogeneous Polynomials. Laura P. Schaposnik and Sebastian Schulz. SIGMA 17 (2021), 079, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862592765982932992 |
|---|---|
| author | Schaposnik, Laura P. Schulz, Sebastian |
| author_facet | Schaposnik, Laura P. Schulz, Sebastian |
| citation_txt | Triality for Homogeneous Polynomials. Laura P. Schaposnik and Sebastian Schulz. SIGMA 17 (2021), 079, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Through the triality of SO(8, ℂ), we study three interrelated homogeneous bases of the ring of invariant polynomials of Lie algebras, which give the bases of three Hitchin fibrations, and identify the explicit automorphisms that relate them.
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| first_indexed | 2026-03-13T21:32:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211344 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T21:32:09Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schaposnik, Laura P. Schulz, Sebastian 2025-12-30T15:51:29Z 2021 Triality for Homogeneous Polynomials. Laura P. Schaposnik and Sebastian Schulz. SIGMA 17 (2021), 079, 14 pages 1815-0659 2020 Mathematics Subject Classification: 14H60; 31A35; 33C80; 53C07 arXiv:2009.13573 https://nasplib.isofts.kiev.ua/handle/123456789/211344 https://doi.org/10.3842/SIGMA.2021.079 Through the triality of SO(8, ℂ), we study three interrelated homogeneous bases of the ring of invariant polynomials of Lie algebras, which give the bases of three Hitchin fibrations, and identify the explicit automorphisms that relate them. The authors are thankful to S. Rayan for his thorough comments on a draft of the manuscript. 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. Both authors are thankful for the support of the Simons Center for Geometry and Physics during the Spring 2019 program on Geometry and Physics of Hitchin systems. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Triality for Homogeneous Polynomials Article published earlier |
| spellingShingle | Triality for Homogeneous Polynomials Schaposnik, Laura P. Schulz, Sebastian |
| title | Triality for Homogeneous Polynomials |
| title_full | Triality for Homogeneous Polynomials |
| title_fullStr | Triality for Homogeneous Polynomials |
| title_full_unstemmed | Triality for Homogeneous Polynomials |
| title_short | Triality for Homogeneous Polynomials |
| title_sort | triality for homogeneous polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211344 |
| work_keys_str_mv | AT schaposniklaurap trialityforhomogeneouspolynomials AT schulzsebastian trialityforhomogeneouspolynomials |