Triality, Exceptional Lie Algebras and Deligne Dimension Formulas: Triality, exceptional Lie algebras and Deligne dimension formulas.
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| Název: | Triality, Exceptional Lie Algebras and Deligne Dimension Formulas: Triality, exceptional Lie algebras and Deligne dimension formulas. |
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| Autoři: | Laurent Manivel, Joseph M. Landsberg |
| Zdroj: | Advances in Mathematics. 171:59-85 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Elsevier BV, 2002. |
| Rok vydání: | 2002 |
| Témata: | Mathematics - Differential Geometry, Mathematics(all), Exceptional (super)algebras, exceptional Lie algebras, 01 natural sciences, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Deligne dimension formulas, triality, FOS: Mathematics, Freudenthal magic square, Representation Theory (math.RT), 0101 mathematics, Algebraic Geometry (math.AG), Simple, semisimple, reductive (super)algebras, Mathematics - Representation Theory |
| Popis: | We give a computer free proof of the Deligne, Cohen and deMan formulas for the dimensions of the irreducible $g$-modules appearing in the tensor powers of $g$, where $g$ ranges over the exceptional complex simple Lie algebras. We give additional dimension formulas for the exceptional series, as well as uniform dimension formulas for other representations distinguished by Freudenthal along the rows of his magic chart. Our proofs use the triality model of the magic square which we review and present a simplified proof of its validity. We conclude with some general remarks about obtaining "series" of Lie algebras in the spirit of Deligne and Vogel. 17 pages |
| Druh dokumentu: | Article |
| Popis souboru: | application/xml |
| Jazyk: | English |
| ISSN: | 0001-8708 |
| DOI: | 10.1006/aima.2002.2071 |
| DOI: | 10.48550/arxiv.math/0107032 |
| Přístupová URL adresa: | http://arxiv.org/abs/math/0107032 https://zbmath.org/1888317 https://doi.org/10.1006/aima.2002.2071 https://www.arxiv-vanity.com/papers/math/0107032/ https://www.sciencedirect.com/science/article/abs/pii/S0001870802920712 https://arxiv.org/pdf/math/0107032 https://dialnet.unirioja.es/servlet/articulo?codigo=314671 https://www.infona.pl/resource/bwmeta1.element.elsevier-5a8fda2f-9b32-3eb8-aa42-90f1ce58bba9 https://www.sciencedirect.com/science/article/pii/S0001870802920712 |
| Rights: | Elsevier Non-Commercial arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....fc28783f54ff092f1ba84189fbd5764e |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | We give a computer free proof of the Deligne, Cohen and deMan formulas for the dimensions of the irreducible $g$-modules appearing in the tensor powers of $g$, where $g$ ranges over the exceptional complex simple Lie algebras. We give additional dimension formulas for the exceptional series, as well as uniform dimension formulas for other representations distinguished by Freudenthal along the rows of his magic chart. Our proofs use the triality model of the magic square which we review and present a simplified proof of its validity. We conclude with some general remarks about obtaining "series" of Lie algebras in the spirit of Deligne and Vogel.<br />17 pages |
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| ISSN: | 00018708 |
| DOI: | 10.1006/aima.2002.2071 |