Weyl group

Conjugation of a Weyl element

Let be a root system, and be the group of all invertible linear endomorphisms leaving invariant, i.e.

Then the Weyl group of is a normal subgroup of , in particular for any and geo

Therewithal¹

Proof

proof

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Footnotes

1. 1972. Introduction to Lie Algebras and Representation Theory, §9.2, p. 43 ↩