Multiplicity formulas for representations of transformation groupoids

Multiplicity formulas for representations of transformation groupoids AbstractWe study the representations of transitive transformation groupoids with the aim of generalizing the Mackey theory. Using the Mackey theory and a bijective correspondence between the imprimitivity systems and the representations of a transformation groupoid we derive the irreducibility theory. Then we derive the direct sum decomposition for representations of a groupoid together with the formula for the multiplicity of subrepresentations. We discuss a physical interpretation of this formula. Finally, we prove the claim analogous to the Peter-Weyl theorem for a noncompact transformation groupoid. We show that the representation theory of a transitive transformation groupoids is closely related to the representation theory of a compact groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

Multiplicity formulas for representations of transformation groupoids

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Publisher
De Gruyter Open
Copyright
© 2017 Artur Giżycki and Leszek Pysiak
ISSN
0420-1213
eISSN
2391-4661
D.O.I.
10.1515/dema-2017-0004
Publisher site
See Article on Publisher Site

Abstract

AbstractWe study the representations of transitive transformation groupoids with the aim of generalizing the Mackey theory. Using the Mackey theory and a bijective correspondence between the imprimitivity systems and the representations of a transformation groupoid we derive the irreducibility theory. Then we derive the direct sum decomposition for representations of a groupoid together with the formula for the multiplicity of subrepresentations. We discuss a physical interpretation of this formula. Finally, we prove the claim analogous to the Peter-Weyl theorem for a noncompact transformation groupoid. We show that the representation theory of a transitive transformation groupoids is closely related to the representation theory of a compact groups.

Journal

Demonstratio Mathematicade Gruyter

Published: Apr 25, 2017

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