An Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras

Abstract

We first present an Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras ${\hat{Y}}_{r,n}(q)$ to give a new proof of the fact, which was previously proved by Chlouveraki and Sécherre, that ${\hat{Y}}_{r,n}(q)$ is a particular case of the pro-$p$-Iwahori-Hecke algebras defined by Vignéras, meanwhile, we give one application. Using the new presentation, we then give a third presentation of ${\hat{Y}}_{r,n}(q),$ 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.

This is the first paper of a series. Further applications of the presentations are clarified in follow-up work