Pacific Journal of Mathematics

Symplectic-Whittaker models for ${\rm Gl}_n$.

Michael J. Heumos and Stephen Rallis

Article information

Source
Pacific J. Math., Volume 146, Number 2 (1990), 247-279.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102645157

Mathematical Reviews number (MathSciNet)
MR1078382

Zentralblatt MATH identifier
0752.22012

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Citation

Heumos, Michael J.; Rallis, Stephen. Symplectic-Whittaker models for ${\rm Gl}_n$. Pacific J. Math. 146 (1990), no. 2, 247--279. https://projecteuclid.org/euclid.pjm/1102645157


Export citation

References

  • [Ba-Ka-S] E. Bannai, N. Kawanaka and S. Song, The character table of the Hecke algebra H(G\2n{Fq),Sp2n(Fq)), preprint, July 1988.
  • [Be-Ze,l] E. Bannai,l] E. Bannai,l] E. Bannai,l] I. N. Bernstein and A. V. Zelevinskii, Representations of the Group G\(n, F) where F is a Non-archimedean Local Field,Russ. Math. Sur- veys, 31, no. 3 (1976), 1-68.
  • [Be-Ze,2] E. Bannai,2] E. Bannai,2] E. Bannai,2] , Induced representations of reductive p-adic groups, I, Ann. Scient. E. Norm. Sup., Fourth series, 10 (1977), 441-472.
  • [Bo-Wa] A. Borel and N. Wallach, Continuous Cohomology, DiscreteSubgroups and Representations of Reductive Groups,Annals of Math. Studies, no.
  • [94] Princeton University Press, Princeton, 1980.
  • [Car] P. Cartier, Representations of p-adic groups: A survey, in Automorphic Forms, Representations of L-functions, A Borel, W. Casselman, editors, AMS Proc. of Symp. in Pure Math., no. 9 (1966), 149-158.
  • [Ca] R. W. Carter, Finite Groupsof Lie Type. Conjugacy Classesand Complex Characters,Wiley-Interscience, J. W. Wiley & Sons, 1985.
  • [Cas] W. Casselman, Introduction to the theory of admissible representations of p-adic reductivegroups, Mimeographed notes, Vancouver, 1975.
  • [Ge-Ka,l] W. Casselman,l] W. Casselman,l] W. Casselman,l] I. M. Gefand and D. A. Kazhdan, Representations of G\(n, K) in Lie Groupsand their Representations 2, Akademiai Kiado, Budapest, 1974.
  • [Ge-Ka,2] W. Casselman,2] W. Casselman,2] W. Casselman,2] , Representations of the group G\(n, K), where K is a local field, Funkt. Anal, i Prilozen., 6, no. 4, (1972), 73-74.
  • [Ge-PS] S. Gelbart and I. Piatetski-Shapiro, L-functions for GxGl(rc),in Explicit Construction of Automorphic L-Functions, Lecture Notes in Mathemat- ics, no. 1254, Springer-Verlag, 1987.
  • [Ja-Sh] H. Jacquet and J. Shalika, The Whittaker models of inducedrepresenta- tions, Pacific J. Math., 109 (1983), 107-120.
  • [Ka-Pa] D. A. Kazhdan and S. J. Patterson,Metaplectic Forms, Pub. Institut des Hautes Etudes Scient., no. 59, 1984.
  • [Kl] A. A. Klyachko, Models for the complex representations of the groups G\{n, q), Math. USSR Sbornik, 48 no. 2, 1984.
  • [Mo-Wa] C. Moeglin and J. L. Waldspurger, Modeles de Whittaker degenerespour desgroupes p-adiques, MathematischeZeitschrift, 196, (1987), 427-452.
  • [PS-Ra] I. Piatetskii-Shapiro and Stephen Rallis, L-functions for the Classical Groups, in Explicit Construction of Automorphic L-Functions. Lecture Notes in Mathematics, no. 1254, Springer-Verlag, 1987.
  • [Ro] F. Rodier, Whittaker models for admissible representations of reductive p-adic split groups, in Harmonic Analysis on Homogeneous Spaces, C. C. Moore, ed., AMS Proc.of Symp. in Pure Math.,no. 26, (1973), 425-430.
  • [Se] J.-P. Serre, Cohomologie Galoisienne, 2nd ed., Lecture Notes in Mathe- matics, vol. 5, Springer-Verlag, 1964.
  • [Sp] T. Springer, Galois cohomology of linear algebraicgroups, in Algebraic Groupsand Discontinuous Groups, A. Borel, G.D.Mostow, editors, AMS Proc. of Symp. in Pure Math., no. 9, (1966), 149-158.
  • [Ta,l] T. Springer,l] T. Springer,l] T. Springer,l] M. Tadic, Unitary dual of p-adic G\(). Proof of Bernstein's conjecture, Bull. Amer. Math. Soc, (New Series), 13, no. 1, (July 1985), 39-42.
  • [Ta,2] T. Springer,2] T. Springer,2] T. Springer,2] , Topology of unitary dual of nonarchimedean G\{), Duke Math. J., 55, no. 2, (1987), 385-422.
  • [Ta,3] T. Springer,3] T. Springer,3] T. Springer,3] , Classification of unitary representations in irreducible representa- tions of general linear group {nonarchimedean case), Ann. Scient. Ec. Norm. Sup. 4e serie, t. 19, (1986), 335-382.
  • [Ze] A. V. Zelevinskiy, Induced representations of reductive p-adic groupsII. On irreducible representations of G\(n), Ann. Scient. Ec. Norm. Sup., Fourth series, 13 (1980), 165-210.