Crystal isomorphisms and wall-crossing maps for rational Cherednik algebras

Nicolas Jacon (1) , Cédric Lecouvey (2)

1 LMR - Laboratoire de Mathématiques de Reims
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

We show that the wall crossing bijections between simples of the category O of the rational Cherednik algebras reduce to particular crystal isomorphisms which can be computed by a simple combinatorial procedure on multipartitions of fixed rank.

Domaines: Théorie des représentations [math.RT]

Nicolas Jacon, Cédric Lecouvey. Crystal isomorphisms and wall-crossing maps for rational Cherednik algebras. Transformation Groups, 2018, 23, pp.101-117. ⟨10.1007/s00031-016-9402-9⟩. ⟨hal-01283858v3⟩