Geodesic
The Weyl group of a~graded Lie algebra
Izvestiya. Mathematics , Tome 10 (1976) no. 3, pp. 463-495

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The action of the group $G_0$ of fixed points of a semisimple automorphism $\theta$ of a reductive algebraic group $G$ on an eigenspace $V$ of this automorphism in the Lie algebra $\mathfrak g$ of the group $G$ is considered. The linear groups which are obtained in this manner are called $\theta$-groups in this paper; they have certain properties which are analogous to properties of the adjoint group. In particular, the notions of Cartan subgroup and Weyl group can be introduced for $\theta$-groups. It is shown that the Weyl group is generated by complex reflections; from this it follows that the algebra of invariants of any $\theta$-group is free. Bibliography: 30 titles. 
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     author = {\`E. B. Vinberg},
     title = {The {Weyl} group of a~graded {Lie} algebra},
     journal = {Izvestiya. Mathematics },
     pages = {463--495},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_3_a2/}
}
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È. B. Vinberg. The Weyl group of a~graded Lie algebra. Izvestiya. Mathematics , Tome 10 (1976) no. 3, pp. 463-495. http://geodesic.mathdoc.fr/item/IM2_1976_10_3_a2/