Journal of Advances in Mathematics and Computer Science

On the Weyl Approach to Tensor Representations of Exceptional Lie Groups: The Case of G2 and F4

Luis J. Boya *

Department of Física Teórica, University of Zaragoza, E-50009 Zaragoza, Spain.

R. Campoamor-Stursberg

I.M.I. and Geometría y Topología, Complutense University of Madrid, E-28040 Madrid, Spain.

*Author to whom correspondence should be addressed.

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Abstract

An attempt is made to approach the irreducible representations of the exceptional Lie groups G₂ and F₄ by symmetrization of some defining representations by means of Young tableaux, procedure that works rather well for most of the classical groups. For G₂ the program is completely successful, while it is not quite so for F₄. As the five exceptional Lie groups are related to octonions, we also comment on the “octonion” character of these two groups, in particular the relation of F₄ to some other connected Spin groups.

Keywords: Exceptional Lie algebra, representation, tensor product, Weyl method.

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