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arXiv 2012.153842020-12-31math.RT

Groupoids, Geometric Induction and Gelfand Models

Anne-Marie Aubert, Antonio Behn, Jorge Soto-Andrade

备注：: 10 pages. To be submitted to J. Group Theory

英文摘要：

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 $2$.

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