We study the action of the Weyl group of type
acting as permutations on the set of weights of the minuscule representation of type
(also
known as the spin representation). Motivated by a previous work, we seek to
determine when cycle structures alone reveal the irreducibility of these minuscule
representations. After deriving formulas for the simple reflections viewed as
permutations, we perform a series of computer-aided calculations in GAP. We are
then able to establish that, for certain ranks, the irreducibility of the minuscule
representation cannot be detected by cycle structures alone.
