论文标题
在紧凑的离散估值环上对通用线性组表示的归纳方法
An inductive approach to representations of general linear groups over compact discrete valuation rings
论文作者
论文摘要
Andrey Zelevinsky在1981年发表的数学讲义中，引入了一个新的Hopf代数家族，他称之为{\ em em psh-algebras}。这些代数旨在捕获对称群体和经典群体的表示理论。这种结构的要旨是将诸如归纳和限制的代表性操作及其抛物线变体转化为代数和煤层操作，例如乘法和集合。例如，Mackey公式将作为代数侧的HOPF公理重新分配。在本文中，我们采取了实质性步骤，以使这些想法适应一般线性群体，而不是紧凑的离散估值环。我们构建了一个类似的双gebra，其中包含一个大的PSH-Elgebra，该代数扩展了Zelevinsky的代数，用于在有限场上的一般线性基团的情况下。我们证明了几种基本变化结果，这些结果与离散估值环的扩展有关代数。
In his seminal Lecture Notes in Mathematics published in 1981, Andrey Zelevinsky introduced a new family of Hopf algebras which he called {\em PSH-algebras}. These algebras were designed to capture the representation theory of the symmetric groups and of classical groups over finite fields. The gist of this construction is to translate representation-theoretic operations such as induction and restriction and their parabolic variants to algebra and coalgebra operations such as multiplication and comultiplication. The Mackey formula, for example, is then reincarnated as the Hopf axiom on the algebra side. In this paper we take substantial steps to adapt these ideas for general linear groups over compact discrete valuation rings. We construct an analogous bialgebra that contains a large PSH-algebra that extends Zelevinsky's algebra for the case of general linear groups over finite fields. We prove several base change results relating algebras over extensions of discrete valuation rings.
