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Preliminaries

  • Roger Howe
  • Eng Chye Tan
Part of the Universitext book series (UTX)

Abstract

In this section some facts are collected on the structure theory of Lie groups and Lie algebras. We will be brief and almost no proofs will be given. For more details and proofs, see the books by Adams [1], Helgason [2], and Varadarajan [2]. For most purposes, the paper by Howe [5] treats Lie groups in an elementary way and provides the basic facts required for this book. We will not need too much “high technology”, and the reader is safe if he keeps thinking of SL(2, ℝ) and its Lie algebra sl(2, R) (to be defined later). The advanced reader may skip this chapter.

Keywords

Unitary Representation Haar Measure Polynomial Growth Maximal Compact Subgroup Irreducible Unitary Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Roger Howe
    • 1
  • Eng Chye Tan
    • 2
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Department of MathematicsNational University of SingaporeSingapore

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