Mathematics > Representation Theory
[Submitted on 26 May 2014 (v1), last revised 14 Aug 2016 (this version, v7)]
Title:Yokonuma-Schur algebras
View PDFAbstract: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.
Submission history
From: Weideng Cui [view email][v1] Mon, 26 May 2014 00:42:45 UTC (13 KB)
[v2] Fri, 6 Jun 2014 08:14:23 UTC (14 KB)
[v3] Fri, 15 Aug 2014 13:47:09 UTC (15 KB)
[v4] Tue, 18 Nov 2014 12:48:13 UTC (16 KB)
[v5] Mon, 1 Dec 2014 06:59:12 UTC (16 KB)
[v6] Tue, 8 Dec 2015 13:21:56 UTC (28 KB)
[v7] Sun, 14 Aug 2016 03:03:09 UTC (35 KB)
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