标题： 一个有限域上一般线性群的双陪集代数 显示英文标题

标题： One algebra of double cosets for a general linear group over a finite field

摘要： 设$\mathbb {F}_q$为具有$q$个元素的有限域。 设$\alpha\leqslant n$为正整数。 考虑一般线性群$\mathrm{GL}(\alpha+n, \mathbb {F}_q) $及其子群$H(n)$，该子群固定$\mathbb {F}_q^{\alpha+n}$中的前$\alpha$个基向量。 表示$\mathcal{A}_n$为$H(n)$-biinvariant 函数在$\mathrm{GL}(\alpha+n, \mathbb {F}_q) $上的卷积代数。 我们用生成元和关系来描述代数$\mathcal{A}_n$，并证明该族$\mathcal{A}_n$可以自然地插值到任意复数$n$（域$\mathbb {F}_q$和$\alpha$是固定的）。 显示英文摘要

摘要： Let $\mathbb {F}_q$ be finite field with $q$ elements. Let $\alpha\leqslant n$ be positive integers. Consider the general linear group $\mathrm{GL}(\alpha+n, \mathbb {F}_q) $ and its subgroup $H(n)$, which fixes the first $\alpha$ basis elements in $\mathbb {F}_q^{\alpha+n}$. Denote $\mathcal{A}_n$ by the convolution algebra of $H(n)$-biinvariant functions on $\mathrm{GL}(\alpha+n, \mathbb {F}_q) $. We describe algebras $\mathcal{A}_n$ in terms of generators and relations and show that the family $\mathcal{A}_n$ admits a natural interpolation to arbitrary complex $n$ (the field $\mathbb {F}_q$ and $\alpha$ are fixed).