Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
add comment

1 Answer

up vote 8 down vote accepted

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.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.