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Classification of two involutions on compact semisimple Lie groups and root systems. (English) Zbl 0998.22004
This paper is a continuation of the author’s earlier paper [J. Algebra 197, 49-91 (1997; Zbl 0887.22009)]. In this interesting work Matsuki classifies pairs of involutions \((\sigma,\tau)\) of a compact semisimple Lie algebra \(g\) with respect to the corresponding double coset decomposition \(H\backslash G/L\). The author also determines explicitly the root system \(\Sigma,\dim g_c(a, \alpha,\lambda)\) and the Weyl group \(J\) for some representatives of the equivalence classes of \((\sigma,\tau)\), when \(G\) is simply connected.

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