I'm studying the article of Kac "Lie Superalgebras" (1974) and in several times he use the fact that if $L$ is a semisimple Lie Algebra, $V$ its faithful, irreducible and finite-dimensional module with $\lambda$ highest weight and $\mu$ lowest weight. Then if $2\lambda$ or $\lambda - \mu$ are a root of $L$ then $L$ must be simple. I have no clue why this is true, can someone help me?
2026-03-25 09:31:45.1774431105
Relation between higher and lower weight ans simplicity
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