论文标题
限制从复杂群体到真实形式的表示形式
Restricting Representations from a Complex Group to a Real Form
论文作者
论文摘要
令$ g $为一个复杂的连接还原代数组，让$ g _ {\ mathbb {r}} $为$ g $的真实形式。我们从$ g $的$ g $ from $ g $构造一系列函数$ l_i \ mathcal {r} $从$ g _ {\ mathbb {r}} $的$ g $的$ g $表示。我们建立了这些函子的许多基本特性，包括它们在无穷小特征，相关的多样性以及对最大紧凑型亚组的限制方面的行为。我们推断每个$ l_i \ Mathcal {r} $将$ g $的单一表示表示为$ g _ {\ mathbb {r}} $的单位表示。以$ l_i \ Mathcal {r} $的交替总和，我们在字符级别上获得了明确定义的同构。当$ g _ {\ mathbb {r}} $被拆分时，我们计算此同构。
Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp. finite-length) representations of $G_{\mathbb{R}}$. We establish many basic properties of these functors, including their behavior with respect to infinitesimal character, associated variety, and restriction to a maximal compact subgroup. We deduce that each $L_i\mathcal{R}$ takes unipotent representations of $G$ to unipotent representations of $G_{\mathbb{R}}$. Taking the alternating sum of $L_i\mathcal{R}$, we get a well-defined homomorphism on the level of characters. We compute this homomorphism in the case when $G_{\mathbb{R}}$ is split.
