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Duality of induction and restriction for abelian twisted covariant systems

Published online by Cambridge University Press:  24 October 2008

Siegfried Echterhoff
Siegfried Echterhoff
Affiliation:
Universität-Gesamihochschule Paderborn, Fachbereich Mathematik-Informatik, Warburgerstrasse 100, D-33098 Paderborn, Germany
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Abstract

Let (A, G, α, τ) be a twisted covariant system such that G/Nτ is abelian, and let Nτ ⊆ M ⊆ H be closed subgroups of G. We show that inducing covariant representations from A ⋊α, τM to A ⋊α, τH is in a certain sense dual to restricting representations from (A⋊α, τG)⋊άM┴ to (A⋊α, τG)⋊άH┴, and that, similarly, restricting representations from A⋊α, τH to A⋊α, τM is dual to inducing representations from (A⋊τG)⋊άH┴ to (A ⋊α, τG)⋊άM┴.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 2 , September 1994 , pp. 301 - 315
Copyright
Copyright © Cambridge Philosophical Society 1994

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