تقرير
Iwahori-Hecke algebras acting on tensor space by $q$-deformed letter permutations and $q$-partition algebras
| العنوان: | Iwahori-Hecke algebras acting on tensor space by $q$-deformed letter permutations and $q$-partition algebras |
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| المؤلفون: | Thangavelu, Geetha, Dipper, Richard |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, 20C15, 20D15(Primary), 20C33, 20D20 (Secondary) |
| الوصف: | Let $R$ be a commutative ring with identity and let $V$ be a free $R$-module of rank $n$ for some $n\in\mathbb{N}$. Fixing an $R$-basis $\mathcal{E}$ of $V$, the symmetric group $\mathfrak{S}_n$ acts on $V$ by permuting $\mathcal{E}$ and hence on tensor space $V^{\otimes r}$ for $r\in\mathbb{N}$ via the usual tensor product action turning $V$ and $V^{\otimes r}$ into $R\mathfrak{S}_n$-modules. For units $q$ in $R$ we construct an action of the corresponding Iwahori-Hecke algebra $\mathcal{H}_{R,q}(\mathfrak{S}_n)$ which specializes to the action of $R\mathfrak{S}_n$, if $q$ is taken to $1$. The centralizing algebra of this action is called the $q$-partition algebra $\mathcal{P}_{R,q}(n,r)$. Let $R$ be a field of characteristic not dividing $q$. We prove, that $\mathcal{P}_{R,q}(n,r)$ is isomorphic to the $q$-partition algebra defined by Halverson and Thiem by different means a few years ago. Comment: 21 pages, To appear in Journal of algebra |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.03156 |
| رقم الأكسشن: | edsarx.2311.03156 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |