Exercise 14, § 7

Tag 014Q, permanent. Cite it as [Bourbaki, Tag 014Q].

Lie Groups and Lie Algebras, VIII, 242

Bourbaki marks this one as harder than the rest.

Let $\lambda \in P_{++}, F_{\lambda}$ be the largest proper submodule of $Z(\lambda )$ and $v$ a primitive element of $Z(\lambda )$ of weight $\lambda$ , cf. §6, no. 3. Show that

F_{\lambda}=\sum_{\alpha\in B}U(\mathfrak{g})X_{-\alpha}^{\lambda(H_{\alpha})+1}v=\sum_{\alpha\in B}U(\mathfrak{n}_-)X_{-\alpha}^{\lambda(H_{\alpha})+1}v

Solution

No solution has been written yet.

Cited by

§ 7. Finite dimensional modules over a split semi-simple Lie algebra

Cites

§6, no. 3