  We 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.
