Zelevinsky's involution at roots of unity

Leclerc, B.; Thibon, J. -Y.; Vasserot, E.

Zelevinsky's involution at roots of unity

Authors

Leclerc, B.

Thibon, J. -Y.

Vasserot, E.

Description

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.
17 pages, Latex, epsf macros