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.

the proof of Theorem 5.18 is rewritten. In a forthcoming paper, we define and study the affine Yokonuma-Schur algebra. arXiv admin note: text overlap with arXiv:math/0205143 by other authors

References in corpus (2)

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

Cited by in corpus (1)

• Affine cellularity of quantum affine algebras