Acta Mathematica

Reducibility of generalized principal series representations

Birgit Speh and David A. Vogan

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Acta Math. Volume 145 (1980), 227-299.

Received: 31 March 1978
First available in Project Euclid: 31 January 2017

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1980 © Almqvist & Wiksell


Speh, Birgit; Vogan, David A. Reducibility of generalized principal series representations. Acta Math. 145 (1980), 227--299. doi:10.1007/BF02414191.

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  • Borel, A. & Wallach, N. R., Seminar on the cohomology of discrete subgroups of semsimple groups. Mimeographed notes, Institute for Advanced Study, 1976.
  • Enright, T. J. & Wallach, N. R. The fundamental series of semisimple Lie algebras and semisimple Lie groups. Preprint.
  • Harish-Chandra, Harmonic analysis on real reductive groups I. J. Functional Analysis, 19 (1975), 104–204.
  • —, Harmonic analysis on real reductive groups III. Ann. of Math., 104 (1976), 117–201.
  • —, Representations of semisimple Lie groups III. Trans. Amer. Math. Soc., 76 (1954). 234–253.
  • Hecht H. & Schmid, W., A proof of Blattner's conjecture. Invent. Math., 31 (1975), 129–154.
  • Hirai, T., On irreducible representations of the Lorentz group of n-th order. Proc. Japan Acad., 38 (1962), 83–87.
  • Humphreys, J. E., Introduction to Lie Algebras and Representation Theory. Springer-Verlag, New York, 1972.
  • Jantzen, J. C., Zur Charakterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren. Math. Z., 140 (1974), 127–149.
  • Kostant, B., On the existence and irreducibility of certain series of representations. Bull. Amer. Math. Soc., 75 (1969), 627–642.
  • Knapp, A. W. & Stein, E. M., Singular integrals and the principal series IV. Proc. Nat. Acad. Sci. U.S.A., 72 (1975), 2459–2461.
  • Knapp, A. W. & Zuckerman, G., Classification of irreducible tempered representations of semisimple Lie groups. Proc. Nat. Acad. Sci. U.S.A., 73, (1976), 2178–2180.
  • Langlands, R. P., On the classification of irreducible representations of real algebraic groups. Mimeographed notes. Institute for Advanced Study, 1973.
  • Lepowsky, J., Algebraic results on representations of semisimple Lie groups. Trans. Amer. Math. Soc., 176 (1973), 1–44.
  • Schiffman, G., Intégrales d'entrolacement et fonctions de Whittaker. Bull. Soc. Math. France, 99 (1971), 3–72.
  • Schmid, W., On the characters of the discrete series (the Hermitian symmetric case). Invent. Math., 30 (1975), 47–144.
  • —, Two character identities for semisimple Lie groups, in Non-commutative Harmonic Analysis. Lecture Notes in Mathematics 587, Springer-Verlag, Berlin, 1977.
  • Speh, B., Some results on pricipal series for GL(n, R). Ph.D. Dissertation, Massachusetts Institute of Technology, June, 1977.
  • Vogan, D., The algebraic structure of the representations of semisimples Lie groups. Ann. of Math., 109 (1979), 1–60.
  • Warner, G., Harmonic Analysis of Semisimple Lie Groups 1. Springer-Verlag, New York, 1972.
  • Zuckerman, G., Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. of Math. 106 (1977), 295–308.