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Proceedings of the American Mathematical Society

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Spectra in representations of semisimple Lie group


Author: Sidney C. Scull
Journal: Proc. Amer. Math. Soc. 41 (1973), 287-293
MSC: Primary 22E45
DOI: https://doi.org/10.1090/S0002-9939-1973-0376967-0
MathSciNet review: 0376967
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Abstract: The spectrum of the infinitesimal generator of a one-parameter group of unitary operators arising from a representation of a semisimple Lie group is determined. The support of the spectral measure depends only on whether the group is a group of automorphisms of a bounded symmetric domain.


References [Enhancements On Off] (What's this?)

  • [1] Harish-Chandra, Representations of semi-simple Lie groups. V, Amer. J. Math. 78 (1956), 1-41. MR 18, 490. MR 0082055 (18:490c)
  • [2] S. Helgason, Differential geometry and symmetric spaces, Pure and Appl. Math., vol. 12, Academic Press, New York, 1962. MR 26 #2986. MR 0145455 (26:2986)
  • [3] N. Jacobson, Lie algebras, Interscience Tracts in Pure and Appl. Math., no. 10, Interscience, New York, 1962. MR 26 #1345. MR 0143793 (26:1345)
  • [4] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57-110 = Russian Math. Surveys 17 (1962), no. 4, 53-104. MR 25 #5396. MR 0142001 (25:5396)
  • [5] C. C. Moore, Ergodicity of flows on homogeneous spaces, Amer. J. Math. 88 (1966), 154-178. MR 33 #1409. MR 0193188 (33:1409)
  • [6] E. Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572-615. MR 21 #5901. MR 0107176 (21:5901)
  • [7] H. Rossi and M. Vergne, Functions holomorphes de carré sommable sur un domaine de Siegel et étude de la série discrete holomorphe, C. R. Acad. Sci. Paris 275 (3 juillet 1972). MR 0301243 (46:401)
  • [8] W. Schmid, Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Rüumen, Invent. Math. 9 (1969/70), 61-80. MR 41 #3806. MR 0259164 (41:3806)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0376967-0
Keywords: Unitary representation, spectral measure, semisimple Lie group
Article copyright: © Copyright 1973 American Mathematical Society

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