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Integral pairings and Dynkin indices. (English) Zbl 0689.22008

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

MSC:

22E46 Semisimple Lie groups and their representations
17B20 Simple, semisimple, reductive (super)algebras
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