# Quantum affine wreath algebras

## TL;DR

This paper introduces quantum affine wreath algebras, a new class of algebras that generalize affine Hecke algebras and affine wreath algebras through deformation techniques, and explores their structural properties.

## Contribution

It defines quantum affine wreath algebras associated with symmetric algebras and investigates their structure and cyclotomic quotients.

## Key findings

- Established the structure theory of quantum affine wreath algebras
- Analyzed the properties of their cyclotomic quotients
- Connected these algebras to existing algebraic frameworks

## Abstract

To each symmetric algebra we associate a family of algebras that we call quantum affine wreath algebras. These can be viewed both as symmetric algebra deformations of affine Hecke algebras of type $A$ and as quantum deformations of affine wreath algebras. We study the structure theory of these new algebras and their natural cyclotomic quotients.