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We first give a direct proof of a basis theorem for the cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q).$ Our approach follows Kleshchevs, which does not use the representation theory of $Y_{r,n}^{d}(q),$ and so it is very different from that of [ChP2]. We also present two applications. Then we prove that the cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q)$ is cellular by constructing an explicit cellular basis, and show that the Jucys-Murphy elements for $Y_{r,n}^{d}(q)$ are JM-elements in the abstract sense. In the appendix, we shall develop the fusion procedure for $Y_{r,n}^{d}(q).$
We establish an explicit algebra isomorphism between the affine Yokonuma-Hecke algebra $widehat{Y}_{r,n}(q)$ and a direct sum of matrix algebras with coefficients in tensor products of affine Hecke algebras of type $A.$ As an application of this resu
We explore the modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras. We provide an equivalence between the category of finite dimensional representations of the affine (resp. cyclotomic) Yokonuma-Hecke algebra and that of an
Inspired by the work [PA], we establish an explicit algebra isomorphism between the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q)$ and a direct sum of matrix algebras over tensor products of degenerate cyclotomic Hecke algebras of type
We give two different approaches to classifying the simple modules of $0$-Yokonuma-Hecke algebras $Y_{r,n}(0)$ over an algebraically closed field of characteristic $p$ such that $p$ does not divide $r.$ Using the isomorphism between the $0$-Yokonuma-
Inspired by the work [Ra1], we directly give a complete classification of irreducible calibrated representations of affine Yokonuma-Hecke algebras $widehat{Y}_{r,n}(q)$ over $mathbb{C},$ which are indexed by $r$-tuples of placed skew shapes. We then