Yokonuma-Schur algebras

Abstract

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 $\text{Y}_{r,n}(q).$ 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 $\text{YS}_{q}(r,n).$ In the appendix, we define and study the cyclotomic Yokonuma-Schur algebra in a similar way.