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Lie Theory and Geometry pp 167–215Cite as

Birkhäuser

Familles cohérentes sur les groupes de Lie semi-simples et restriction aux sous-groupes compacts maximaux

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Part of the book series: Progress in Mathematics ((PM,volume 123))

Abstract

Let G be a semi-simple simply connected Lie group and K be a subgroup, maximal among the subgroups compact modulo the center. Invariant eigendistributions on G can be restricted to K. It is an irritating fact that, without supplementary assumptions, this restriction does not determine the distribution. However, we prove here that this is true if, instead of a single invariant eigendistribution, one considers a family of invariant eigendistributions, coherent in the sense of W. Schmid. We also study non connected semi-simple groups: we define a notion of coherent family of invariant eigendistributions and prove a unicity theorem in this setting.

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Author information

Authors and Affiliations

  1. Université Paris 7-Denis Diderot et URA 748 du C.N.R.S., France

    Michel Duflo

  2. E.N.S. et UA 762 du C.N.R.S., France

    Michèle Vergne

Authors
  1. Michel Duflo
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  2. Michèle Vergne
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Penn State University, 16802, University Park, PA, USA

    Jean-Luc Brylinski  & Ranee Brylinski  & 

  2. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    Victor Guillemin  & Victor Kac  & 

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© 1994 Springer Science+Business Media New York

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Duflo, M., Vergne, M. (1994). Familles cohérentes sur les groupes de Lie semi-simples et restriction aux sous-groupes compacts maximaux. In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics, vol 123. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0261-5_6

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  • DOI: https://doi.org/10.1007/978-1-4612-0261-5_6

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6685-3

  • Online ISBN: 978-1-4612-0261-5

  • eBook Packages: Springer Book Archive

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