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Characters, Bi-Modules and Representations in Lie Group Harmonic Analysis

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Harmonic Analysis and Hypergroups

Part of the book series: Trends in Mathematics ((TM))

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Abstract

This paper is a personal look at some issues in the representation theory of Lie groups having to do with the role of commutative hypergroups, bi-modules, and the construction of representations. We begin by considering Frobenius’ original approach to the character theory of a finite group and extending it to the Lie group setting, and then introduce bi-modules as objects intermediate between characters and representations in the theory. A simplified way of understanding the formalism of geometric quantization, at least for compact Lie groups, is presented, which leads to a canonical bi-module of functions on an integral coadjoint orbit. Some meta-mathematical issues relating to the construction of representations are considered.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of New South Wales, Sydney, 2052, Australia

    N. J. Wildberger

Authors
  1. N. J. Wildberger
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, University of Oregon, 97403, Eugene, OR, USA

    K. A. Ross

  2. Dept. of Mathematics, University of Delhi, Delhi, India

    A. I. Singh

  3. Dept. of Mathematics, University College London, London, UK

    J. M. Anderson

  4. The Institute of Math. Sciences, CIT Campus, Taramani, Chennai, India

    V. S. Sunder

  5. Centre for Optimization and Mathematical Modeling, Institute for Technologies, Moscow, Russia

    G. L. Litvinov

  6. School of Mathematics, Univ. of New South Wales, Sidney, NSW, Australia

    N. J. Wildberger

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© 1998 Springer Science+Business Media New York

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Wildberger, N.J. (1998). Characters, Bi-Modules and Representations in Lie Group Harmonic Analysis. In: Ross, K.A., Singh, A.I., Anderson, J.M., Sunder, V.S., Litvinov, G.L., Wildberger, N.J. (eds) Harmonic Analysis and Hypergroups. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4348-5_14

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  • DOI: https://doi.org/10.1007/978-0-8176-4348-5_14

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4899-0158-3

  • Online ISBN: 978-0-8176-4348-5

  • eBook Packages: Springer Book Archive

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