The <fundamental weights> satisfy
$$
\frac{2\mu_i\mathbin\cdot\alpha_j}{|\alpha_j|^2}=\delta_{ij}.
$$
Solving these equations gives
$$
\boxed{\mu_1=\left(\frac12,\frac{\sqrt3}2\right)
=2\alpha_1+\alpha_2,\qquad
\mu_2=(0,\sqrt3)=3\alpha_1+2\alpha_2}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 1 / v / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-302/1/v/solution