Cyclotomic Yokonuma-Hecke algebras are cyclotomic quiver Hecke algebras

TL;DR

This paper establishes an explicit isomorphism between cyclotomic Yokonuma-Hecke algebras of type A and cyclotomic quiver Hecke algebras, expanding the understanding of their algebraic structures.

Contribution

It proves that cyclotomic Yokonuma-Hecke algebras are isomorphic to cyclotomic quiver Hecke algebras and provides an explicit inverse isomorphism, extending prior results.

Findings

Establishes an explicit isomorphism between the two algebra types.

Uses disjoint cyclic quivers to construct the quiver.

Relates the result to Lusztig's isomorphism.

Abstract

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.