On the exceptional series,and its descendantsLa série exceptionnelle,et sa descendance |
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Authors: | Pierre Deligne Benedict H Gross |
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Affiliation: | 1. School of Mathematics, IAS, Princeton, NJ 08540, USA;2. Department of Mathematics, Harvard University, Cambridge, MA 02138, USA |
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Abstract: | Many of the striking similarities which occur for the adjoint representation of groups in the exceptional series (cf. [1–3]) also occur for certain representations of specific reductive subgroups. The tensor algebras on these representations are easier to describe (cf. [4,5,7]), and may offer clues to the original situation.The subgroups which occur form a Magic Triangle, which extends Freudenthal's Magic Square of Lie algebras. We describe these groups from the perspective of dual pairs, and their representations from the action of the dual pair on an exceptional Lie algebra. To cite this article: P. Deligne, B.H. Gross, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 877–881. |
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