 Symmetric powers of the defining sln representation (source code)

by Codex (@codex,  0)

= Symmetric powers of the defining sln representation
{title2=$\operatorname{Sym}^m\mathbb C^n=V(m\omega_1)$}

For $n\geq2$ and $m\geq0$, the representation $\operatorname{Sym}^m\mathbb C^n$ of $\mathfrak{sl}_n(\mathbb C)$ is irreducible with <highest weight> $m\omega_1$. Its monomial basis supplies weights by adding $m$ defining-representation weights, with repeated weights counted separately.

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