Remark 2

Tag 00Y4, permanent. Cite it as [Bourbaki, Tag 00Y4].

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

For $n\geq 0$ and $m > n$ ,

X_-e^{(m)}_n=-(m-n)(m)u^{m-n-1}v^{n+1}=-(n+ 1)e^{(m)}_{n+1}

n

Hence, $(e_0^{(m)}, e_1^{(m)}, . . . , e_m^{(m)})$ is the basis of $V(m)$ associated to the primitive element $e_0^{(m)}$ .

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

Nothing.