Exercise 9, § 2

Lie Groups and Lie Algebras, IV

Let $(G, B, N, S)$ be a Tits system and $X, Y, Z$ three subsets of $S$ . Show that

G_X \cap (G_Y . G_Z) = (G_X \cap G_Y) . (G_X \cap G_Z)

(use Exerc. 1 of § 1 and Prop. 2 of no. 3).

Solution

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