Braden, H. W. Integral pairings and Dynkin indices. (English) Zbl 0689.22008 J. Lond. Math. Soc., II. Ser. 43, No. 2, 313-323 (1991). We review two related notions of index introduced by Dynkin, one the index of a subgroup or subalgebra in a semi-simple group or algebra and the other being the index of a linear representation of a semi-simple Lie algebra. Amongst other results we give a simple algebraic proof of Dynkin’s theorem that this first index is an integer. Reviewer: H.W.Braden Cited in 1 Document MSC: 22E46 Semisimple Lie groups and their representations 17B20 Simple, semisimple, reductive (super)algebras Keywords:Dynkin indices; indices of semisimple Lie algebras; semi-simple group; linear representation; Dynkin’s theorem PDFBibTeX XMLCite \textit{H. W. Braden}, J. Lond. Math. Soc., II. Ser. 43, No. 2, 313--323 (1991; Zbl 0689.22008) Full Text: DOI