Triality, exceptional Lie algebras and Deligne dimension formulas

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dc.creatorLandsberg, J. M.
dc.creatorManivel, L.
dc.date2001-07-04
dc.date.accessioned2026-07-07T04:42:28Z
dc.date.available2026-07-07T04:42:28Z
dc.descriptionWe 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.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0107032
dc.identifierhttp://arxiv.org/abs/math/0107032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61799
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subjectRepresentation Theory
dc.titleTriality, exceptional Lie algebras and Deligne dimension formulas
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