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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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