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Introduction to the Representation Theory of Compact and Locally Compact Groups

Part of London Mathematical Society Lecture Note Series

  • Date Published: February 1983
  • availability: Available
  • format: Paperback
  • isbn: 9780521289757

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  • Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

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    Product details

    • Date Published: February 1983
    • format: Paperback
    • isbn: 9780521289757
    • length: 216 pages
    • dimensions: 228 x 152 x 13 mm
    • weight: 0.33kg
    • availability: Available
  • Table of Contents

    Part I. Representations of compact groups:
    1. Compact groups and Haar measures
    2. Representations, general constructions
    3. A geometrical application
    4. Finite-dimensional representations of compact groups
    5. Decomposition of the regular representation
    6. Convolution, Plancherel formula & Fourier inversion
    7. Characters and group algebras
    8. Induced representations and Frobenius-Weil reciprocity
    9. Tannaka duality
    10. Representations of the rotation group
    Part II. Representations of Locally Compact Groups:
    11. Groups with few finite-dimensional representations
    12. Invariant measures on locally compact groups and homogeneous spaces
    13. Continuity properties of representations
    14. Representations of G and of L1(G)
    15. Schur's lemma: unbounded version
    16. Discrete series of locally compact groups
    17. The discrete series of S12(R)
    18. The principal series of S12(R)
    19. Decomposition along a commutative subgroup
    20. Type I groups
    21. Getting near an abstract Plancherel formula
    Epilogue.

  • Author

    Alain Robert

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