论文标题
群体素，几何诱导和Gelfand模型
Groupoids, Geometric Induction and Gelfand Models
论文作者
论文摘要
在本文中，我们介绍了一个（有限）组$ g $的子组$ h $的经典表示形式的固有版本，此处称为{\ em几何诱导}，它与任何传递性，不一定是$ g $ g $ -set $ x $相关联的$ x $，并与$ g $ g $ g $ g $ a $ a $ a $ a $ a $ a的任何表示形式相关联。我们表明，在$ g $是对称组或等级$ 2 $的投影性的一般线性群体的情况下，适用于合适的$ g $ - set $ x $的一维字符的几何感应，可为$ g $ $ g $。
In this paper we introduce an intrinsic version of the classical induction of representations for a subgroup $H$ of a (finite) group $G$, called here {\em geometric induction}, which associates to any, not necessarily transitive, $G$-set $X$ and any representation of the action groupoid $A(G,X)$ associated to $G$ and $X$, a representation of the group $G$. We show that geometric induction, applied to one dimensional characters of the action groupoid of a suitable $G$-set $X$ affords a Gelfand Model for $G$ in the case where $G$ is either the symmetric group or the projective general linear group of rank $2$.
