Duke Mathematical Journal

On unitarity of spherical representations

Jesper Bang-Jensen

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Article information

Source
Duke Math. J., Volume 61, Number 1 (1990), 157-194.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077296652

Digital Object Identifier
doi:10.1215/S0012-7094-90-06108-3

Mathematical Reviews number (MathSciNet)
MR1068384

Zentralblatt MATH identifier
0752.22011

Subjects
Primary: 22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
Secondary: 22E46: Semisimple Lie groups and their representations

Citation

Bang-Jensen, Jesper. On unitarity of spherical representations. Duke Math. J. 61 (1990), no. 1, 157--194. doi:10.1215/S0012-7094-90-06108-3. https://projecteuclid.org/euclid.dmj/1077296652


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References

  • [1] J. Bang-Jensen, The multiplicities of certain $K$-types spherical representations, Journal of Functional Analysis (to appear).
  • [2] D. Barbasch, The unitary dual for complex classical Lie groups, Invent. Math. 96 (1989), no. 1, 103–176.
  • [3] K. D. Johnson and N. R. Wallach, Composition series and intertwining operators for the spherical principal series. I, Trans. Amer. Math. Soc. 229 (1977), 137–173.
  • [4] A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups. II, Invent. Math. 60 (1980), no. 1, 9–84.
  • [5] B. Kostant, On the existence and irreducibility of certain series of representations, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 231–329.
  • [6] B. Speh and D. A. Vogan, Jr., Reducibility of generalized principal series representations, Acta Math. 145 (1980), no. 3-4, 227–299.
  • [7] D. A. Vogan, Jr., Representations of real reductive Lie groups, Progress in Mathematics, vol. 15, Birkhäuser Boston, Mass., 1981.
  • [8] D. A. Vogan, Jr., Unitarizability of certain series of representations, Ann. of Math. (2) 120 (1984), no. 1, 141–187.
  • [9] D. A. Vogan, Jr., The unitary dual of $\rm GL(n)$ over an Archimedean field, Invent. Math. 83 (1986), no. 3, 449–505.
  • [10] D. A. Vogan, Jr., Unitary representations of reductive Lie groups, Annals of Mathematics Studies, vol. 118, Princeton University Press, Princeton, NJ, 1987.
  • [11] J. A. Wolf, The action of a real semisimple Lie group on a complex flag manifold. II. Unitary representations on partially holomorphic cohomology spaces, American Mathematical Society, Providence, R.I., 1974.