Annals of Global Analysis and Geometry

, Volume 43, Issue 2, pp 107–121

Invariant four-forms and symmetric pairs


DOI: 10.1007/s10455-012-9336-y

Cite this article as:
Moroianu, A. & Semmelmann, U. Ann Glob Anal Geom (2013) 43: 107. doi:10.1007/s10455-012-9336-y


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.


S-Representations Exceptional Lie algebras Irreducible representations Representation of Lie type 

Mathematics Subject Classification (2000)

Primary 22E46 20C35 15A66 17B25 53C35 57T15 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.CMLS, École PolytechniquePalaiseauFrance
  2. 2.Institut für Geometrie und Topologie, Fachbereich MathematikUniversität StuttgartStuttgartGermany