Pacific Journal of Mathematics

Some qualitative results on the representation theory of ${\rm Gl}_{n}$ over a $p$-adic field.

Roger E. Howe

Article information

Source
Pacific J. Math., Volume 73, Number 2 (1977), 479-538.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102810620

Mathematical Reviews number (MathSciNet)
MR0492088

Zentralblatt MATH identifier
0385.22009

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

Citation

Howe, Roger E. Some qualitative results on the representation theory of ${\rm Gl}_{n}$ over a $p$-adic field. Pacific J. Math. 73 (1977), no. 2, 479--538. https://projecteuclid.org/euclid.pjm/1102810620


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References

  • [1] A. Borel and J. Tits, Groupes Reductifs, Pub. I.H.E.S., 27 (1965), 55-150.
  • [2] F. Bruhat, Distributions sur un groupe localement compact et applications Vetude des representations de groupes p-adiques, Bull. Soc. Math, de France, 89 (1961), 43-76.
  • [3] C. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York, 1962.
  • [4] J. Dixmier, Les C*-algebres et leurs representations, Gauthier-Villars, Paris.
  • [5] W. Casselman, Introductionto the theory of admissible representations of p-adic reductive groups, preprint.
  • [6] R. Godement, A theory of spherical functionsI, T.A.M.S., 73 (1952), 496-556.
  • [7] Harish-Chandra, Invarianteigendistributionson semisimple Lie groups, B.A.M.S., 69 (1963), 117-123.
  • [8] Harish-Chandra, Discrete Series for Semisimple Lie Groups, II, Acta Math., 116 (1966), 1-111.
  • [9] Harish-Chandra, Harmonic Analysis on Reductive p-adic Groups, notes by G. van Dijk, Springer Lecture Notes 162, Springer Verlag, New York, 1970.
  • [10] Harish-Chandra, Harmonic Analysis on Reductive p-adic Groups, Harmonic Analysison Homogeneous Spaces, PSPM vol. XXVI, Amer. Math. Soc, Providence, 1973.
  • [11] R. Howe, The Fourier transformand germs of characters, Math. Ann., 208 (1974), 305-322.
  • [12] R. Howe, Tamely ramified supercuspidal representationsof Gln, Pacific J. Math., 73 (1977), 437-460.
  • [13] R. Howe, On the principal series of Gln over p-adic fields, Trans. Amer. Math. Soc, 177 (1973), 275-286. 141Kirillov theory for compact p-adic groups, Pacific J. Math., 73 (1977), 365-381.
  • [15] R. Howe, On the character of Weil's representation, T.A.M.S., 177 (1973), 287-298.
  • [16] H. Jacquet and R. P. Langlands, Automorphic Forms on Gh, Springer Lecture Notes 114, Springer-Verlag, New York, 1970.
  • [17] I. G. MacDonald, Spherical functionson a p-adic semisimple group, Lecture notes, Madras, 1972.
  • [18] G. W. Mackey, The theory of group representations, Lecture notes, Univ. of Chicago, 1955.
  • [19] C. Rader, Ph. D. Thesis, U. of Washington at Seattle, 1971.
  • [20] P. Samuel and O. Zariski, Commutative Algebra, Vol. I, Van Nostrand, New York, 1960.
  • [21] I. N. Bernstein, All reductive p-adic groups are of type I (Russian), Functional Analysis i. Pril., 8 no. 2, (1974), 3-6.
  • [22] G. van Dijk, Computation of certain induced characters of p-adic groups, Math. Ann., 199 (1972), 229-240.
  • [23] N. Wallach, Cyclic vectors and irreducibilityfor principalseriesrepresentations, T.A.M.S., 164 (1972), 389-396.
  • [24] A. Weil, Sur certains groupes d'operateursunitaires,Acta Math., I l l (1964), 143-211.