An Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras

TL;DR

This paper introduces a new Iwahori-Matsumoto presentation for affine Yokonuma-Hecke algebras, providing a new proof of their relation to pro-p-Iwahori-Hecke algebras and revealing that the extended affine Hecke algebra of type A is a subalgebra.

Contribution

It presents a novel Iwahori-Matsumoto presentation for affine Yokonuma-Hecke algebras, offering new insights and connections to extended affine Hecke algebras.

Findings

Affine Yokonuma-Hecke algebra is a case of pro-p-Iwahori-Hecke algebra

New presentation leads to the discovery of a subalgebra isomorphic to extended affine Hecke algebra of type A

Provides a new proof of the algebra's properties and relations

Abstract

We first present an Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras $\widehat{Y}_{r,n}(q)$ to give a new proof of the fact, which was previously proved by Chlouveraki and S\'echerre, that $\widehat{Y}_{r,n}(q)$ is a particular case of the pro-$p$-Iwahori-Hecke algebras defined by Vign\'eras, meanwhile, we give one application. Using the new presentation, we then give a third presentation of $\widehat{Y}_{r,n}(q),$ from which we immediately get an unexpected result, that is, the extended affine Hecke algebra of type $A$ is a subalgebra of the affine Yokonuma-Hecke algebra.