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The Origins of Infinite Dimensional Unitary Representations of Lie Groups

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The Intersection of History and Mathematics

Part of the book series: Science Networks · Historical Studies ((SNHS,volume 15))

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Abstract

The systematic investigation of infinite dimensional unitary representations of Lie groups began with the works of V. Bargmann[1947] on SL(2, R) and I. M. Gelfand-M. A. Naimark[1947] on SL(2,C). The theory of the finite dimensional representations of Lie algebras and Lie groups had been established by E. Cartan[1913] and H. Weyl[1925/26], [1934/35]. However the finite dimensional theory did not develop spontaneously into the infinite dimensional one. The purpose of this paper is to study the circumstances.

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Authors
  1. Sugiura Mitsuo
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Editors and Affiliations

  1. Department of History & Philosophy of Science, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153, Japan

    Ch. Sasaki

  2. Tsuda College, 2-1-1, Tsuda-cho, Kodaira-shi, Tokyo 187, Japan

    M. Sugiura (Vice-Chairman) (Vice-Chairman)

  3. Program in History, The Graduate Center, CUNY, 33 West 42nd Street, 10036-8099, New York, NY, USA

    J. W. Dauben (Chairman) (Chairman)

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© 1994 Birkhäuser Verlag

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Mitsuo, S. (1994). The Origins of Infinite Dimensional Unitary Representations of Lie Groups. In: Sasaki, C., Sugiura, M., Dauben, J.W. (eds) The Intersection of History and Mathematics. Science Networks · Historical Studies, vol 15. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7521-9_15

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  • DOI: https://doi.org/10.1007/978-3-0348-7521-9_15

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7523-3

  • Online ISBN: 978-3-0348-7521-9

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