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Isotropy Subgroups of Transformation Groups

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Abstract

In this paper we consider transitive actions of Lie groups on analytic manifolds. We study three cases of analytic manifolds and their corresponding transformation groups. Given a free action on the left, we define left orbit spaces and consider actions on the right by maximal compact subgroups. We show that these actions are transitive and find the corresponding isotropy subgroups. Further, we show that the left orbit spaces are reductive homogeneous spaces. This article thus forms the basis of a forthcoming paper on invariant differential operators on homogeneous manifolds.

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Author notes

  1. Dmitriy Khots

    Present address: West Corporation, 7171 Mercy Rd, Omaha, NE, 68106, USA

Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Dmitriy Khots & Tuong Ton-That

Authors
  1. Dmitriy Khots
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  2. Tuong Ton-That
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Correspondence to Dmitriy Khots.

Additional information

Partially supported by a Carver Research Initiative Grant.

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Khots, D., Ton-That, T. Isotropy Subgroups of Transformation Groups. Acta Appl Math 100, 269–289 (2008). https://doi.org/10.1007/s10440-007-9184-0

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  • DOI: https://doi.org/10.1007/s10440-007-9184-0

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