论文标题
A型iwahori-Hecke代数的稳定中心
Stable Centres of Iwahori-Hecke Algebras of type A
论文作者
论文摘要
Farahat和Higman的著名结果构建了一个代数$ \ Mathrm {fh} $，该$ intherpolate''中心$ z（\ mathbb {z} s_n）$ s_n $的代数代数。我们将这些结果从对称组代数扩展到类型$ a $ iwahori-hecke代数，$ h_n（q）$。特别是，我们解释了如何构建一个代数$ \ mathrm {fh} _q $“ interpolating”中心$ z（h_n（q））$。我们证明$ \ mathrm {fh} _q $是同构至$ \ nathcal {r} [q，q，q^{ - 1}] \ otimes _ {\ mathbb {z}}}λ$（其中$ \ \ \ \ \ \米{r} $是$ \ nrec {r} $ iss $ iss $ is unome unomial and unomial and unomir and unomir and youn anommial and unomir and和功能）。同构可以描述为“ Jucys-Murphy元素的评估”，从而证明了弗朗西斯和王的猜想。在SpecHt模块上作用时，这会产生$ z（h_n（q））$的Geck-Rouquier基础的字符公式。
A celebrated result of Farahat and Higman constructs an algebra $\mathrm{FH}$ which "interpolates" the centres $Z(\mathbb{Z}S_n)$ of group algebras of the symmetric groups $S_n$. We extend these results from symmetric group algebras to type $A$ Iwahori-Hecke algebras, $H_n(q)$. In particular, we explain how to construct an algebra $\mathrm{FH}_q$ "interpolating" the centres $Z(H_n(q))$. We prove that $\mathrm{FH}_q$ is isomorphic to $\mathcal{R}[q,q^{-1}] \otimes_{\mathbb{Z}} Λ$ (where $\mathcal{R}$ is the ring of integer-valued polynomials, and $Λ$ is the ring of symmetric functions). The isomorphism can be described as "evaluation at Jucys-Murphy elements", leading to a proof of a conjecture of Francis and Wang. This yields character formulae for the Geck-Rouquier basis of $Z(H_n(q))$ when acting on Specht modules.
