2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77031We give a combinatorial algorithm for computing Zelevinsky's involution of the set of isomorphism classes of irreducible representations of the affine Hecke algebra $\H_m(t)$ when $t$ is a primitive $n$th root of 1. We show that the same map can also be interpreted in terms of aperiodic nilpotent orbits of $\Zb/n\Zb$-graded vector spaces.17 pages, Latex, epsf macrosQuantum Algebratext