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

  • N. J. Wildberger
Conference paper
Part of the Trends in Mathematics book series (TM)


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.


Line Bundle Irreducible Representation Irreducible Character Coadjoint Orbit Circle Bundle 


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • N. J. Wildberger
    • 1
  1. 1.School of MathematicsUniversity of New South WalesSydneyAustralia

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