论文标题
真实古典群体的特殊单体表示：计数和减少
Special unipotent representations of real classical groups: counting and reduction
论文作者
论文摘要
让$ g $成为Harish-Chandra班上真正的还原群体。我们将相干持续表示理论的一些后果带入了具有给定的无穷小特征的$ g $不可还原表示的计数和复杂相关品种的给定界限。当$ g $是一个真正的古典群体（包括真正的元容器组）时，我们研究了Arthur和Barbasch-Vogan的意义，研究了$ \ check {\ check {\ Mathcal O} $的$ G $的特殊单位表示。这里$ \ check {\ mathcal o} $是$ g $的Langlands dual（或$ g $的Metaplectik dual of $ g $时）的nilpotent伴随轨道。我们为附加到$ \ check {\ Mathcal O} $的$ g $的特殊单位表示的数量进行精确计数。我们还将构建与$ \ check {\ Mathcal O} $相关的特殊独立表示的问题减少到当$ \ check {\ mathcal o} $分析上甚至是分析的情况下（对于真实的古典群体等效，在M – Gllin的意义上具有良好的奇偶性）。该论文是两篇论文中的第一本，内容涉及对真实古典群体的特殊独立表示的分类。
Let $G$ be a real reductive group in Harish-Chandra's class. We derive some consequences of theory of coherent continuation representations to the counting of irreducible representations of $G$ with a given infinitesimal character and a given bound of the complex associated variety. When $G$ is a real classical group (including the real metaplectic group), we investigate the set of special unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. Here $\check{\mathcal O}$ is a nilpotent adjoint orbit in the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We give a precise count for the number of special unipotent representations of $G$ attached to $\check{ \mathcal O}$. We also reduce the problem of constructing special unipotent representations attached to $\check{\mathcal O}$ to the case when $\check{\mathcal O}$ is analytically even (equivalently for a real classical group, has good parity in the sense of Mœglin). The paper is the first in a series of two papers on the classification of special unipotent representations of real classical groups.
