Corollary

Tag 00YD, permanent. Cite it as [Bourbaki, Tag 00YD].

Lie Groups and Lie Algebras, chapter VIII, § 1. The Lie algebra sl(2, k) and its representations

Let $E = E'\oplus E''$ be the decomposition of E defined in the Cor. of Prop. 2. The element $(-10)$ of $\mathbf{S}\mathbf{L}(2, k)$ operates by +1 on $E'$

0 $-1$

and by $-1$ on $E''$ .

This follows from (ii), applied to $t=-1$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Cor. of Prop. 2