2014/05/26 by Weideng Cui, Cui, Weideng · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1405.6441
openalex publication_date 2014/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we define the Yokonuma-Schur algebra YSq(r,n) as the endomorphism algebra of a permutation module for the Yokonuma-Hecke algebra Yr,n(q). We prove that YSq(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 Yr,n(q) in the sense of Rouquier following [HM2]. We also introduce the tilting modules for YSq(r,n). In the appendix, we define and study the cyclotomic Yokonuma-Schur algebra in a similar way.