Affine cellularity of affine Yokonuma-Hecke algebras

Abstract

We establish an explicit algebra isomorphism between the affine Yokonuma-Hecke algebra ${\hat{Y}}_{r,n}(q)$ and a direct sum of matrix algebras with coefficients in tensor products of affine Hecke algebras of type $A.$ As an application of this result, we show that ${\hat{Y}}_{r,n}(q)$ is affine cellular in the sense of Koenig and Xi, and further prove that it has finite global dimension when the parameter $q$ is not a root of the Poincaré polynomial. As another application, we also recover the modular representation theory of ${\hat{Y}}_{r,n}(q)$ previously obtained in [CW].

We give the details of the proofs of some lemmas

References in corpus (2)

• Cell structures for the Yokonuma-Hecke algebra and the algebra of braids and ties
• Cellularity of cyclotomic Yokonuma-Hecke algebras