Pacific Journal of Mathematics

On some explicit formulas in the theory of Weil representation.

R. Ranga Rao

Article information

Source
Pacific J. Math., Volume 157, Number 2 (1993), 335-371.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102634748

Mathematical Reviews number (MathSciNet)
MR1197062

Zentralblatt MATH identifier
0794.58017

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 11F27: Theta series; Weil representation; theta correspondences 20G25: Linear algebraic groups over local fields and their integers 22E35: Analysis on $p$-adic Lie groups

Citation

Ranga Rao, R. On some explicit formulas in the theory of Weil representation. Pacific J. Math. 157 (1993), no. 2, 335--371. https://projecteuclid.org/euclid.pjm/1102634748


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References

  • [1] N. Bourbaki, Algebres,Chapter 9, Hermann, Paris, 1959.
  • [2] F. Bruhat, Distributions sur un groupe localement compact et applications, Bull. Soc. Math, de France, 89 (1961), 43-75.
  • [3] P. Cartier, Uber enige Integral formeln in der theorie der quadratische formen, Math. Z., 84(1964), 93-100.
  • [4] S. S. Gelbart, Weil's Representation and the Spectrum of the MetaplecticGroup, Lecture Notes in Math., vol. 530, Springer-Verlag, New York, 1976.
  • [5] Paul Gerardin, Weil representations associated to finite fields, J. Algebra, 46 (1977), 54-102.
  • [6] V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys no. 14, Amer. Math. Soc, Providence, RI, 1977.
  • [7] T. Kubota, Topological coveringof SL(2) overa localfield,J. Math. Soc. Japan, 19(1967), 114-121.
  • [8] Jean Leray, Complement a la theorie d'Arnold de indice de Maslov, Symposia Math., XIV (1974), 33-53.
  • [9] G. Lion, Integrales Interlacement sur des Groupes de Lie Nilpotents et Indices de Maslov, Lecture Notes in Math., vol. 587, Springer-Verlag, New York, 1977, pp. 160-177.
  • [10] G. W. Mackey, The theory of unitary representations,Chicago Lectures in Math., Chicago Univ. Press, 1976.
  • [11] S. Rallis and G. Schiffman, Distribution Invariant par le Groupe Orthogonal, Lecture Notes in Math., vol. 497, Springer-Verlag, New York, 1975, pp. 494- 643.
  • [12] M. Saito, Representations unitaires des groupes symplectiques, J. Math. Soc. Japan, 24(1972), 232-252.
  • [13] I. E. Segal, Transformsfor operatorsand symplectic automorphisms overalocally compact abelian group, Math. Scand., 12-13 (1963), 31-43.
  • [14] J. P. Serre, A Course in Arithmetic, Springer, New York, 1973.
  • [15] D. Shale, Linear symmetries offree boson fields, Trans. Amer. Math. Soc, 103 (1962), 149-167.
  • [16] A. Weil, Sur certaines groupes d'operateurs unitaires, Acta Math., 11 (1964), 143-211.
  • [17] N. R. Wallach, Symplectic Geometry and Fourier Analysis, Math. Sci. Press, Brookline, Massachusetts, 1977.
  • [18] C. C. Moore, Group extensions of p-adic and adelic linear groups, I.H. E. S., 1968.
  • [19] G. B. Folland, Harmonic analysis in phase space,Ann. of Math. Studies, Prince- ton University Press, 1989.
  • [20] G. Lion and M. Vergne, The Weil representationMaslov index and Theta series, Progress in Math., vol. 6, Birkhauser, Boston, 1980.
  • [21] C. Moeglin, M. F. Vigneras, and J. L. Waldspurger, Correspondencesde Howe sur un Corps p-adique, Lecture Notes in Math., vol. 1291, Springer-Verlag, Berlin, 1987.