On the classification of irreducible low rank unitary representations of classical groups

Jian-Shu Li

Compositio Mathematica (1989)

  • Volume: 71, Issue: 1, page 29-48
  • ISSN: 0010-437X

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Li, Jian-Shu. "On the classification of irreducible low rank unitary representations of classical groups." Compositio Mathematica 71.1 (1989): 29-48. <http://eudml.org/doc/89967>.

@article{Li1989,
author = {Li, Jian-Shu},
journal = {Compositio Mathematica},
keywords = {symplectic group; local field; type I classical groups; low rank representations},
language = {eng},
number = {1},
pages = {29-48},
publisher = {Kluwer Academic Publishers},
title = {On the classification of irreducible low rank unitary representations of classical groups},
url = {http://eudml.org/doc/89967},
volume = {71},
year = {1989},
}

TY - JOUR
AU - Li, Jian-Shu
TI - On the classification of irreducible low rank unitary representations of classical groups
JO - Compositio Mathematica
PY - 1989
PB - Kluwer Academic Publishers
VL - 71
IS - 1
SP - 29
EP - 48
LA - eng
KW - symplectic group; local field; type I classical groups; low rank representations
UR - http://eudml.org/doc/89967
ER -

References

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  4. 4 R. Howe, L2-duality in the stable range, Preprint. 
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  6. 6 R. Howe, θ series and invariant theory, Proc. Symp. Pure Math., Vol. 33, A.M.S., (1979). Zbl0423.22016
  7. 7 R. Howe, Small unitary representations of classical groups, In: Group representations, ergodic theory, operator algebras and math. physics. Proceedings of a conference in honor of G.W. Mackey, C.C. Moore, (eds.) M.S.R.I., Publ. No. 6, Springer-Verlag, New York (1986) pp. 121-150. Zbl0635.22014MR880374
  8. 8 R. Howe and C. Moore, Asymptotic properties of unitary representations, J. Func. Anal.32 (1979) 72-96. Zbl0404.22015MR533220
  9. 9 R. Howe and Piatetski-Shapiro, A counterexample to the generalized Ramanujan Conjecture, in Proc. Symp. Pure. Math., Vol. 33, A.M.S. (1979). Zbl0423.22018
  10. 10 D. Kazhdan, Some applications of the Weil representation, Journal d'Analyse Mathematique32 (1977) 235-248. Zbl0445.22018MR492089
  11. 11 N. Kurokawa, Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two. Invent. Math.49 (1978) 149-165. Zbl0397.10018MR511188
  12. 12 P. Kutzko and P.J. Salley, Jr., Supercuspidal Representations of SL2, preprint. 
  13. 13 R.P. Langlands, Automorphic representations, Shimura varieties and motives, ein märchen. Proc. Symp. Pure. Math., Vol. 33, A.M.S. (1979). Zbl0447.12009MR546619
  14. 14 J. Li, Non-existence of singular cusp forms, preprint. Zbl0768.11017
  15. 15 J. Li, Distinguished cusp form are theta series, preprint. Zbl0689.10041
  16. 16 J. Li, Singular unitary representations of classical groups, preprint. Zbl0694.22011
  17. 17 I.I. Piatetski-Shapiro, Distinguished representations and Tate theory for reductive groups, Proceedings, International Congress of Mathematicians, Helsinki, (1978). Zbl0443.12003
  18. 18 S. Rallis and G. Schiffmann, Représentation Supercuspidales du groupe Métaplectique, J. Math.Kyoto Univ., 17(3) (1977). Zbl0398.22023MR498395
  19. 19 R. Scaramuzzi, On a notion of rank for unitary representations of general linear groups, Thesis, Yale (1985). Zbl0704.22012
  20. 20 W. Scharlau, Quadratic and Hermitian Forms, Springer-Verlag (1985). Zbl0584.10010MR770063
  21. 21 D. Vogan, Unitary Representations of reductive Lie Groups, Ann. Math. Studies118 (1987). Zbl0626.22011MR908078
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  24. 24 Z.X. Wan, On the commutator subgroup of the unitary group. Sci. Rec.4 (1960), 343-348. Zbl0098.25304MR130305
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  26. 26 A. Weil, Sur la formulae de Siegel dans la theorie des groupes classiques, Acta Math.113 (1965) 1-87. Zbl0161.02304MR223373

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