Invariant Four-forms and Symmetric Pairs

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Date
2012-04-24MFO Scientific Program
Research in Pairs 2012Series
Oberwolfach Preprints;2012,03Author
Moroianu, Andrei
Semmelmann, Uwe
Metadata
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Abstract
We give criteria for real, complex and quaternionic representations to define $s$-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations whose second exterior power is irreducible or has an irreducible summand of co-dimension one, and we give a conceptual computation-free argument for the construction of the exceptional Lie algebras of compact type.