GROUPOIDS, GEOMETRIC INDUCTION AND GELFAND MODELS
Abstract
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 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.
Domains
Mathematics [math]
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