A construction of unitary representations in parabolic rank two

M. W. Baldoni-Silva; A. W. Knapp

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 4, page 579-601
  • ISSN: 0391-173X

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Baldoni-Silva, M. W., and Knapp, A. W.. "A construction of unitary representations in parabolic rank two." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.4 (1989): 579-601. <http://eudml.org/doc/84063>.

@article{Baldoni1989,
author = {Baldoni-Silva, M. W., Knapp, A. W.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {unitary representations; complementary series representations; connected semisimple linear Lie group; induced representation; intertwining operators; semidefiniteness},
language = {eng},
number = {4},
pages = {579-601},
publisher = {Scuola normale superiore},
title = {A construction of unitary representations in parabolic rank two},
url = {http://eudml.org/doc/84063},
volume = {16},
year = {1989},
}

TY - JOUR
AU - Baldoni-Silva, M. W.
AU - Knapp, A. W.
TI - A construction of unitary representations in parabolic rank two
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 4
SP - 579
EP - 601
LA - eng
KW - unitary representations; complementary series representations; connected semisimple linear Lie group; induced representation; intertwining operators; semidefiniteness
UR - http://eudml.org/doc/84063
ER -

References

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  1. [1] M.W. Baldoni-Silva - A.W. Knapp, Unitary representations induced from maximal parabolic subgroups, J. Func. Anal.69 (1986), 21-120. Zbl0614.22004MR864757
  2. [2] M.W. Baldoni-Silva - A.W. Knapp, Intertwining operators and unitary representations I, J. Func. Anal., 82 (1989), 151-236. Zbl0683.22010MR976317
  3. [3] A.U. Klimyk - A.M. Gavrilik, The representations of the groups U(n, 1) and SO(n, 1), preprint ITP-76-39E, Institute for Theoretical Physics, Kiev, USSR, 1976. Zbl0337.22020MR579617
  4. [4] A.W. Knapp, Weyl group of a cuspidal parabolic, Ann. Sci. Ecole Norm. Sup.8 (1975), 275-294. Zbl0305.22010MR376963
  5. [5] A.W. Knapp, Commutativity of intertwining operators for semisimple groups, Compositio Math.46 (1982), 33-84. Zbl0488.22027MR660154
  6. [6] A.W. Knapp, Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton Univ. Press, Princeton, N.J., 1986. Zbl0604.22001MR855239
  7. [7] A.W. Knapp - B. Speh, Status of classification of irreducible unitary representations, "Harmonic Analysis", Lecture Notes in Math., No. 908, 1-38, Springer-Verlag, Berlin, 1982. Zbl0496.22018MR654177
  8. [8] A.W. Knapp - E.M. Stein, Intertwining operators for semisimple groups, Ann. of Math.93 (1971), 489-578. Zbl0257.22015MR460543
  9. [9] A.W. Knapp - E.M. Stein, Intertwining operators for semisimple groups II, Invent. Math.60 (1980), 9-84. Zbl0454.22010MR582703
  10. [10] A.W. Knapp - G.J. Zuckerman, Classification of irreducible tempered representations of semisimple groups, Ann. of Math.116 (1982), 389-501, and 119 (1984), 639. Zbl0516.22011MR672840
  11. [11] H. Schlichtkrull, Eigenspaces of the Laplacian on hyperbolic spaces: composition series and integral transforms, J. Func. Anal.70 (1987), 194-219. Zbl0617.43005MR870761
  12. [12] B. Speh - D.A. Vogan, Reducibility of generalized principal series representations, Acta Math.145 (1980), 227-299. Zbl0457.22011MR590291
  13. [13] N.R. Wallach, Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, New York, 1973. Zbl0265.22022MR498996
  14. [14] G. Zuckerman, Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. of Math.106 (1977), 295-308. Zbl0384.22004MR457636

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