Let $G_{\mathbb{R}}$ be the set of real points of a complex linear reductive group and ${\hat{G}}_{\lambda }$, its classes of irreducible admissible representations with infinitesimal integral regular character λ. In this case, each cell of representations is associated to a special nilpotent orbit. This helps organize the corresponding set of irreducible Harish-Chandra modules. The goal of this paper is to bypass the need for the character table of the Weyl group associated with ${\hat{G}}_{\lambda }$ in the Springer correspondence, by describing a new and less computationally intensive parametrization of irreducible representations of simple complex Weyl groups.

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外尔群的签名和特征

让 $G_{\mathbb{电阻}}$ 是复线性归约群的实点集，并且 ${\widehat{G}}_{\lambda }$，其具有无穷小积分正则特征λ的不可约可容许表示类。在这种情况下，表示的每个单元格都与一个特殊的幂零轨道相关联。这有助于组织相应的不可约 Harish-Chandra 模块集。本文的目标是绕过与 Weyl 群相关的字符表的需要${\widehat{G}}_{\lambda }$ 在 Springer 的对应关系中，通过描述简单复杂 Weyl 群的不可约表示的一种新的、计算强度较低的参数化。