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The unitary dual ofG 2

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References

  1. Arthur, J.: On some problems suggested by the trace formula. In: Herb, R., Lipsman, R., Rosenberg, J. (eds.) Lie group representations II. (Lecture Notes in Mathematics, vol. 1041). Berlin Heidelberg New York: Springer, 1983, pp. 1–49

    Google Scholar 

  2. Barbasch, D., Vogan, D.: Unipotent representations of complex semisimple Lie groups. Ann. Math.121, 41–110 (1985)

    Google Scholar 

  3. Beilinson, A.: Localization of representations of reductive Lie algebras. In: Proceedings of the International Congress of Mathematicians, Warsaw 1983. Amsterdam London, 1984, pp. 699–710

  4. Brylinski, R., Kostant, B.: Nilpotent orbits, normality, and Hamiltonian group actions (Preprint)

  5. Duflo, M.: Représentations unitaires irréductibles des groupes semi-simples complexes de rang deux. Bull. Soc. Math. Fr.107, 55–96 (1979)

    Google Scholar 

  6. Enright, T.J., Wallach, N.R.: Notes on homological algebra and representations of Lie algebras. Duke Math. J.47, 1–15 (1980)

    Google Scholar 

  7. Gelfand, S.I.: Weil's representation of the Lie algebra of typeG 2, and representations ofSL 3 connected with it. Funct. Anal. Appl.14, 40–41 (1980)

    Google Scholar 

  8. Harish-Chandra: Harmonic analysis on reductive groups I. The theory of the constant term. J. Func. Anal.19, 104–204 (1975)

    Google Scholar 

  9. Huang, J.-S.: The unitary dual of the universal covering group ofGL(n 1ℝ). Duke Math. J.61, 705–745 (1990)

    Google Scholar 

  10. Jantzen, J.C.: Moduln mit einem Höchsten Gewicht. (Lecture Notes in Mathematics, vol. 750). Berlin Heidelberg New York: Springer, 1979

    Google Scholar 

  11. Joseph, A.: The minimal orbit in a simple Lie algebra and its associated maximal ideal. Ann. Sci. Ecole Norm. Sup. (4)9, 1–30 (1976)

    Google Scholar 

  12. Knapp, A.: Representation theory of real semisimple groups: an overview based on examples. Princeton University Press, Princeton, New Jersey, 1986

    Google Scholar 

  13. Knapp, A., Stein, E.: Intertwining operators for semisimple groups II. Invent. Math.60, 9–84 (1980)

    Google Scholar 

  14. Knapp, A.: Lie group, Lie algebras, and cohomology. (Mathematical Notes, vol. 34. Princeton University Press. Princeton, New Jersey, 1988

    Google Scholar 

  15. Kostant, B.: The principle of triality and a distinguished unitary representation ofSO(4,4). 65–109 in: Differential Geometrical Methods in Theoretical Physics (K. Bleuler and M. Werner, eds.). Kluwer Academic Publishers, Dordrecht-Boston, 1988

    Google Scholar 

  16. Langlands, R.P.: On the classification of representations of real algebraic group. In: Representation theory and harmonic analysis on semisimple Lie groups. (Mathematical Surveys and Monographs, vol. 31). American Mathematical Society, Providence, Rhode Island 1989, pp. 101–170

    Google Scholar 

  17. Levasseur, T., Smith, S.P.: Primitive ideals and nilpotent orbits in typeG 2. J. Algebra114, 81–105 (1988)

    Google Scholar 

  18. Pukanszky, L.: The Plancherel formula for the universal covering group ofSL(2, ℝ). Math. Ann.156 (1964) 96–143

    Google Scholar 

  19. Speh, B., Vogan, D.: Reducibility of generalized principal series representations. Acta Math.145, 227–299 (1980)

    Google Scholar 

  20. Vogan, D.: Gelfand-Kirillov dimension for Harish-Chandra modules. Invent. Math.48, 75–98 (1978)

    Google Scholar 

  21. Vogan, D.: The algebraic structure of the representations of semisimple Lie groups I. Ann. Math.109, 1–60 (1979)

    Google Scholar 

  22. Vogan, D.: Irreducible characters of semisimple Lie groups I. Duke Math. J.46, 61–108 (1979)

    Google Scholar 

  23. Vogan, D.: Representations of Real Reductive Lie Groups. Boston Basel Stuttgart: Birkhäuser, 1981

    Google Scholar 

  24. Vogan, D.: Singular unitary representations. In: Carmona, J., Vergne, M. (eds.) Non-commutative harmonic analysis and Lie groups. (Lecture Notes in Mathematics, vol. 880). Berlin Heidelberg New York: Springer, 1981, pp. 506–535

    Google Scholar 

  25. Vogan, D.: Understanding the unitary dual. In: Herb, R., Lipsman, R., Rosenberg, J. (eds.) Lie Group Representations I. (Lecture Notes in Mathematics, vol. 1024). Berlin Heidelberg New York: Springer 1983, pp. 264–286

    Google Scholar 

  26. Vogan, D.: Irreducible characters of semisimple Lie groups III. Proof of the Kazhdan-Lusztig conjectures in the integral case. Invent. Math.71, 381–417 (1983)

    Google Scholar 

  27. Vogan, D.: Unitarizability of certain series of representations. Ann. Math.120, 141–187 (1984)

    Google Scholar 

  28. Vogan, D.: The unitary dual ofGL(n) over an archimedean field. Invent. Math.83, 449–505 (1986)

    Google Scholar 

  29. Vogan, D.: Unitary representations of reductive Lie groups. (Annals of Mathematics Studies, vol. 118). Princeton, New Jersey: Princeton University Press, 1987

    Google Scholar 

  30. Vogan, D.: Associated varieties and unipotent representations. In: Barker, W., Sally, P. (eds.) Harmonic analysis on reductive groups. Boston Basel Berlin: Birkhäuser, 1991

    Google Scholar 

  31. Vogan, D.: Unipotent representations and cohomological induction (Preprint)

  32. Vogan, D. and G. Zuckerman: Unitary representations with non-zero cohomology. Compositio Math.53, 51–90 (1984)

    Google Scholar 

  33. Wong, H.: Dolbeault cohomologies and Zuckerman modules associated with finite rank representations. Ph.D. dissertation, Harvard University, 1991

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Dedicated to Professor Armand Borel, with respect and admiration

Oblatum 6-IV-1993

Research supported in part by the National Science Foundation under grant no. DMS-9011483

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Vogan, D.A. The unitary dual ofG 2 . Invent Math 116, 677–791 (1994). https://doi.org/10.1007/BF01231578

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