Weight string
= Weight string
{title2=$q-p=\langle\mu,\alpha^\vee\rangle$}
For a finite-dimensional representation of a complex <semisimple Lie algebra>, the weights on a line $\mu+\mathbb Z\alpha$ form a contiguous string from $\mu+p\alpha$ to $\mu-q\alpha$, with $q-p=\langle\mu,\alpha^\vee\rangle$. Restriction to the associated sl2 subalgebra gives nested strings of the same parity, so the string endpoints determine the weight set but not its multiplicities.