Cyclotomic Yokonuma–Hecke algebras are cyclotomic quiver Hecke algebras

Salim Rostam (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We prove that cyclotomic Yokonuma–Hecke algebras of type A are cyclotomic quiver Hecke algebras and we give an explicit isomorphism with its inverse, using a similar result of Brundan and Kleshchev on cyclotomic Hecke algebras. The quiver we use is given by disjoint copies of cyclic quivers. We relate this work to an isomorphism of Lusztig.

Mots clés: Quiver Hecke algebras; Hecke algebras; Yokonuma–Hecke algebras

Domaines: Théorie des représentations [math.RT]

Salim Rostam. Cyclotomic Yokonuma–Hecke algebras are cyclotomic quiver Hecke algebras. Advances in Mathematics, 2017, 311, pp.662-729. ⟨10.1016/j.aim.2017.03.004⟩. ⟨hal-01628497v2⟩