The <highest weight of a representation> is the weight $\Lambda$ of a nonzero <weight vector> annihilated by every positive-root operator. Every other weight is obtained from $\Lambda$ by subtracting a nonnegative integer combination of <simple root>[simple roots]. A finite-dimensional irreducible representation of a complex semisimple Lie algebra is determined by its dominant integral highest weight.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 302 / 4 / a / v / Solution

 Solution (source code)