Degenerate principal series representations of S p ( 2 n , 𝐑 )

Soo Teck Lee

Compositio Mathematica (1996)

  • Volume: 103, Issue: 2, page 123-151
  • ISSN: 0010-437X

How to cite


Lee, Soo Teck. "Degenerate principal series representations of $Sp(2n, \mathbf {R})$." Compositio Mathematica 103.2 (1996): 123-151. <>.

author = {Lee, Soo Teck},
journal = {Compositio Mathematica},
keywords = {representations; symplectic groups; Lie algebra; degenerate principal series representations; symplectic form; complementary series; socle series},
language = {eng},
number = {2},
pages = {123-151},
publisher = {Kluwer Academic Publishers},
title = {Degenerate principal series representations of $Sp(2n, \mathbf \{R\})$},
url = {},
volume = {103},
year = {1996},

AU - Lee, Soo Teck
TI - Degenerate principal series representations of $Sp(2n, \mathbf {R})$
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 103
IS - 2
SP - 123
EP - 151
LA - eng
KW - representations; symplectic groups; Lie algebra; degenerate principal series representations; symplectic form; complementary series; socle series
UR -
ER -


  1. 1 Alperin, J.: Diagrams for modules, J. Pure Appl. Algebra16 (1980) 111-119. Zbl0425.16027MR556154
  2. 2 Bargmann, V.: Irreducible unitary representations of the Lorentz group, Ann. of Math.48 (1947) 568-640. Zbl0045.38801MR21942
  3. 3 Bernstein, I.N., Gelfand, I.M. and Gelfand, S.I.: Model of representations of Lie groups, Sel. Math. Sov.1 (1981) 121-142. Zbl0499.22004
  4. 4 Carter, R.: Raising and lowering operators for Sln, with applications to orthogonal bases of Slnmodules, in The Arcata Conference on Representations of Finite Groups, Proc. Sympos. Pure Math.47, Part 2, 351-366, Amer. Math. Soc., Providence, 1987. Zbl0656.20042MR933425
  5. 5 Carter, R. and Lusztig, G.: On the modular representations of the general linear and symmetric groups, Math. Z.136 (1974) 193-242. Zbl0298.20009MR354887
  6. 6 Goodearl, K. and Warfield, R.: An Introduction to Noncommutative Rings, LondonMathematical Society student Texts16, Cambridge University Press, Cambridge, 1989. Zbl0679.16001MR1020298
  7. 7 Howe, R. and Lee, S.: Degenerate principal series representations of GL(n, C) and GL(n, R), in preparation. 
  8. 8 Howe, R. and Tan, E.: Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations, Bull. Amer. Math. Soc.28 (1993) 1-74. Zbl0794.22012MR1172839
  9. 9 Johnson, K.: Degenerate principal series on tube type domains, Contemp. Math.138 (1992) 175-187. Zbl0789.22027MR1199127
  10. 10 Kudla, S. and Rallis, S.: Degenerate principal series and invariant distributions, Israel J. Math.69 (1990) 25-45. Zbl0708.22005MR1046171
  11. 11 Lee, S.: On some degenerate principal series representations of U(n, n), J. of Funct. Anal.126 (1994) 305-366. Zbl0829.22026MR1305072
  12. 12 Sahi, S.: Unitary representations on the Shilov boundary of a symmetric tube domain, in Representations of Groups and Algebras, Contemp. Math.145 (1993) 275-286, Amer. Math. Soc., Providence. Zbl0790.22010MR1216195
  13. 13 Sahi, S.: Jordan algebras and degenerate principal series, preprint. Zbl0822.22006MR1329899
  14. 14 Varadarajan, V.: An Introduction to Harmonic Analysis on Semisimple Lie Groups, Cambridge Studies in Advanced Mathematics, Vol 16, Cambridge Univ. Press, Cambridge, 1989. Zbl0753.22003MR1071183
  15. 15 Wallach, N.R.: Real Reductive Groups I, Academic Press, 1988. Zbl0666.22002MR929683
  16. 16 Zhang, G.: Jordan algebras and generalized principal series representation, preprint. Zbl0829.22023MR1343649

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