We show that the Iwahori–Hecke algebras ${\mathcal{H}}_n$ of type $A_{n-1}$ satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley–Lieb algebras, are the first time that the techniques of homological stability have been applied to algebras that are not group algebras.

中文翻译：

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Iwahori-Hecke 代数的同调稳定性

我们证明了 Iwahori-Hecke 代数${\mathcal{H}}_n$类型${\mathrm{一个}}_{n-1}$满足同调稳定性，其中同调被解释为适当的 Tor 群。我们的结果精确地恢复了 Nakaoka 在定义参数等于 1 的情况下对对称群的同调稳定性结果。我们相信这篇论文以及我们与 Boyd 在 Temperley-Lieb 代数上的联合工作是第一次将同调稳定性已应用于不是群代数的代数。