A categorical equivalence between affine Yokonuma-Hecke algebras and some quiver Hecke algebras

TL;DR

This paper establishes a categorical equivalence between affine Yokonuma-Hecke algebras and certain quiver Hecke algebras, extending previous theoretical frameworks in algebra representation theory.

Contribution

It provides an explicit categorical equivalence between these two algebraic structures, generalizing Rouquier's theorem to new classes of algebras.

Findings

Categorical equivalence between affine Yokonuma-Hecke and quiver Hecke algebras.

Extension of Rouquier's equivalence theorem to affine type A.

Generalization to disjoint copies of quivers of affine type A.

Abstract

Inspired by the work of Rostam, we establish an explicit categorical equivalence between affine Yokonuma-Hecke algebras and quiver Hecke algebras associated to disjoint copies of quivers of (affine) type $A,$ generalizing Rouquier's categorical equivalence theorem.