# Quantum Affine Wreath Algebras

### Daniele Rosso

Department of Mathematics and Actuarial Science, Indiana University Northwest, Gary, IN 46408, USA### Alistair Savage

Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada

## 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.

## Cite this article

Daniele Rosso, Alistair Savage, Quantum Affine Wreath Algebras. Doc. Math. 25 (2020), pp. 425–456

DOI 10.4171/DM/753