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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.

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