Triality, exceptional Lie algebras and Deligne dimension formulas
Algebraic Geometry
2007-05-23 v1 Differential Geometry
Representation Theory
Abstract
We give a computer free proof of the Deligne, Cohen and deMan formulas for the dimensions of the irreducible -modules appearing in the tensor powers of , where 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.
Cite
@article{arxiv.math/0107032,
title = {Triality, exceptional Lie algebras and Deligne dimension formulas},
author = {J. M. Landsberg and L. Manivel},
journal= {arXiv preprint arXiv:math/0107032},
year = {2007}
}
Comments
17 pages