# Highest weight of a trivial representation of a Lie algebra.

Let $g$ be a Lie algebra. $\mathbb{C}$ is a trivial representation of $g$. What is the highest weight of $\mathbb{C}$? I think the weight is the function $f: \mathfrak{h} \to \mathbb{C}$ such that $f(h)=1$ for all $h \in \mathfrak{h}$. Can we express $f$ using fundamental weights?

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In the trivial representation, there is only one weight (it takes the value $0$ on all of $\mathfrak{h}$), so it is automatically the highest weight of this representation.