Yokonuma-Schur algebras

In this paper, we define the Yokonuma-Schur algebra ${\text{YS}}_q(r,n)$ as the endomorphism algebra of a permutation module for the Yokonuma-Hecke algebra ${\text{Y}}_{r,n}(q)\mathrm{.}$ We prove that ${\text{YS}}_q(r,n)$ is cellular by constructing an explicit cellular basis following the approach in [DJM], and we further show that it is a quasi-hereditary cover of ${\text{Y}}_{r,n}(q)$ in the sense of Rouquier following [HM2]. We also introduce the tilting modules for ${\text{YS}}_q(r,n)\mathrm{.}$ In the appendix, we define and study the cyclotomic Yokonuma-Schur algebra in a similar way.