✦ LIBER ✦

Triality, Exceptional Lie Algebras and Deligne Dimension Formulas

✍ Scribed by J.M. Landsberg; L. Manivel

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 266 KB
Volume: 171
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2002.2071

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✦ Synopsis

We give a computer-free proof of the Deligne, Cohen and de Man formulas for the dimensions of the irreducible g-modules appearing in g k ; k44; 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.

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