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An Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras (1610.04993v1)
Published 17 Oct 2016 in math.RT
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.