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Infinitesimal Theory of Representations of Semisimple Lie Groups

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Harmonic Analysis and Representations of Semisimple Lie Groups

Part of the book series: Mathematical Physics and Applied Mathematics ((MPAM,volume 5))

Abstract

For any locally compact topological group G satisfying the second axiom of countability, let ℰ(G) be the set of all equivalence classes of irreducible unitary representations of G. Among the central goals of representation theory have been, first of all, to get a good understanding of the structure of ℰ(G); and secondly, once this is done, to do harmonic analysis on G by setting up isomorphisms between suitable spaces of functions and ‘distributions’ on G with the spaces of their ‘Fourier transforms’ defined on ℰ(G). In this generality we are very far from any definitive solution to these problems. However, when G is a reductive group defined over a local field, great progress has been made.

Research partially supported by National Science Foundation Grant MCS 76-05962.

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Authors and Affiliations

  1. University of California, Los Angeles, USA

    V. S. Varadarajan

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  1. V. S. Varadarajan
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J. A. Wolf M. Cahen M. De Wilde

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© 1980 D. Reidel Publishing Company, Dordrecht, Holland

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Varadarajan, V.S. (1980). Infinitesimal Theory of Representations of Semisimple Lie Groups. In: Wolf, J.A., Cahen, M., De Wilde, M. (eds) Harmonic Analysis and Representations of Semisimple Lie Groups. Mathematical Physics and Applied Mathematics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8961-0_5

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  • DOI: https://doi.org/10.1007/978-94-009-8961-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8963-4

  • Online ISBN: 978-94-009-8961-0

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