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Invariant four-forms and symmetric pairs

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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.

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Authors and Affiliations

  1. CMLS, École Polytechnique, UMR 7640 du CNRS, 91128, Palaiseau, France

    Andrei Moroianu

  2. Institut für Geometrie und Topologie, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Uwe Semmelmann

Authors
  1. Andrei Moroianu
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  2. Uwe Semmelmann
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Correspondence to Andrei Moroianu.

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Moroianu, A., Semmelmann, U. Invariant four-forms and symmetric pairs. Ann Glob Anal Geom 43, 107–121 (2013). https://doi.org/10.1007/s10455-012-9336-y

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  • DOI: https://doi.org/10.1007/s10455-012-9336-y

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