Mullineux involution and crystal isomorphisms

Nicolas Jacon (1)

1 LMR - Laboratoire de Mathématiques de Reims

We develop a new approach for the computation of the Mullineux involution for the symmetric group and its Hecke algebra using the notion of crystal isomorphism and the Iwahori-Matsumoto involution for the affine Hecke algebra of type A. As a consequence, we obtain several new elementary combinatorial algorithms for its computation, one of which is equivalent to Xu's algorithm (and thus Mullineux' original algorithm). We thus obtain a simple interpretation of these algorithms and a new elementary proof that they indeed compute the Mullineux involution.

Domaines: Théorie des représentations [math.RT]; Combinatoire [math.CO]

Nicolas Jacon. Mullineux involution and crystal isomorphisms. 2021. ⟨hal-03278927⟩