2012/02/20 by Andrei Moroianu, Uwe Semmelmann · 3 citations
Mathematics · #(g,K)-module #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential geometry #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Irreducible representation #Lie algebra #Representation of a Lie group #Representation theory of SU #Spin representation #math.DG #math.RT #msc:15A66 #msc:17B25 #msc:20C35 #msc:22E46 #msc:53C35 #msc:57T15
paper · pdf · doi:10.1007/s10455-012-9336-y
published in Annals of Global Analysis and Geometry 43(2), 107-121 (Springer Science+Business Media) · 16 pages [v2: references added, last section expanded)
arxiv created 2012/02/20 · openalex publication_date 2012/06/19 · openalex created_date 2016/06/24 · arxiv updated 2019/01/08 · openalex updated_date 2026/08/05
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.