Cellularity of cyclotomic Yokonuma-Hecke algebras

Abstract

We first give a direct proof of a basis theorem for the cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q).$ Our approach follows Kleshchev's, 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 $Y_{r,n}^{d}(q).$

Fusion procedures of cyclotomic Y-H algebras are added in the appendix. In the arXiv:1405.6441, we define and study Yokonuma-Schur algebras and cyclotomic analogues. arXiv admin note: text overlap with arXiv:1208.4884; text overlap with arXiv:1506.00715 by other authors