Exercise 13, § 4

Tag 0AYX, permanent. Cite it as [Bourbaki, Tag 0AYX].

Lie Groups and Lie Algebras, VI

Let V be the hyperplane in $\mathbf{R}^9$ with equation $x_1 + \cdots + x_9 = 0$ . Let R be the subset of V consisting of the points

(2, 2, 2, -1, -1, -1, -1, -1, -1), \quad (-2, -2, -2, 1, 1, 1, 1, 1, 1),

(3, -3, 0, 0, 0, 0, 0, 0, 0)

together with the points obtained from these by permuting the coordinates. Show that R is a root system in V of type $E_8$ .

Solution

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