Exercise 12, § 7

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

Lie Groups and Lie Algebras, VIII, 242

Let $\lambda \in P_{++}$ and let $\mathscr{X}_{\lambda}$ be the set of weights of $E(\lambda )$ . Show that

\mathscr{X}_{\lambda}\subset \lambda -P_{++}

does not hold in general. (Consider, for example, the adjoint representation of $\mathfrak{s}\mathfrak{l}(3, k).$ )

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