A <dominant weight> has nonnegative Dynkin labels. A <dominant integral weight> additionally lies in the <weight lattice>, so all those labels are nonnegative integers.

Solution

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

{wiki=Weight_(representation_theory)#Dominant_integral_weights}

A weight is dominant when all its <Dynkin label>[Dynkin labels] are nonnegative.

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