Induced representations of reductive 𝔭 -adic groups. II. On irreducible representations of GL ( n )

A. V. Zelevinsky

Annales scientifiques de l'École Normale Supérieure (1980)

  • Volume: 13, Issue: 2, page 165-210
  • ISSN: 0012-9593

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Zelevinsky, A. V.. "Induced representations of reductive ${\mathfrak {p}}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$." Annales scientifiques de l'École Normale Supérieure 13.2 (1980): 165-210. <http://eudml.org/doc/82048>.

@article{Zelevinsky1980,
author = {Zelevinsky, A. V.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {p-adic field; general linear group; bialgebra structure; cuspidal irreducible representation; Whittaker models},
language = {eng},
number = {2},
pages = {165-210},
publisher = {Elsevier},
title = {Induced representations of reductive $\{\mathfrak \{p\}\}$-adic groups. II. On irreducible representations of $\{\rm GL\}(n)$},
url = {http://eudml.org/doc/82048},
volume = {13},
year = {1980},
}

TY - JOUR
AU - Zelevinsky, A. V.
TI - Induced representations of reductive ${\mathfrak {p}}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1980
PB - Elsevier
VL - 13
IS - 2
SP - 165
EP - 210
LA - eng
KW - p-adic field; general linear group; bialgebra structure; cuspidal irreducible representation; Whittaker models
UR - http://eudml.org/doc/82048
ER -

References

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  1. [1] I. N. BERNSTEIN and A. V. ZELEVINSKY, Induced Representations of Reductive p-Adic Groups I (Ann. scient. Éc. Norm. Sup., 4e serie, t. 10, 1977, pp. 441-472). Zbl0412.22015MR58 #28310
  2. [2] I. N. BERNSTEIN and A. V. ZELEVINSKY, Representations of the Group GL (n, F), where F is a Local Non-Archimedean Field (Uspekhi Mat. Nauk, Vol. 31, No. 3, 1976, pp. 5-70). Zbl0348.43007MR54 #12988
  3. [3] I. N. BERNSTEIN and A. V. ZELEVINSKY, Induced Representations of the Group GL (n) Over a p-Adic Field (Funkc. Anal. i Priložen., Vol. 10, No. 3, 1976, pp. 74-75). MR54 #12989
  4. [4] I. N. BERNSTEIN, I. M. GELFAND and S. I. GELFAND, The Structure of Representations Generated by Vectors of Highest Weight (Funkc. Anal. i Prilozen, Vol. 5, No. 1, 1971, pp. 1-9). Zbl0246.17008MR45 #298
  5. [5] N. BOURBAKI, Algèbre, Chap. 1 à 3, Hermann, Paris, 1970. Zbl0211.02401
  6. [6] W. CASSELMAN, Introduction to the Theory of Admissible Representations of p-Adic Reductive Groups, preprint. 
  7. [7] P. DELIGNE, Formes modulaires et représentations de GL (2), in Modular Functions of One Variable II (Lecture Notes in Math., 349, Springer-Verlag, 1973). Zbl0271.10032MR50 #240
  8. [8] I. M. GELFAND and D. A. KAZHDAN, Representations of GL (n, K), in Lie Groups and Their Representations, Akadèmiai Kiado, Budapest, 1974. 
  9. [9] R. GODEMENT and H. JACQUET, Zeta-Functions of Simple Algebras (Lecture Notes in Math., 260, Springer-Verlag, 1972). Zbl0244.12011MR49 #7241
  10. [10] M. HALL, Combinatorial Theory, Blaisdell Publ. Comp., 1967. Zbl0196.02401MR37 #80
  11. [11] A. W. KNAPP and G. ZUCKERMAN, Classification of Irreducible Tempered Representations of Semisimple Lie Groups (Proc. Nat. Acad. Sc. U.S.A., Vol. 73, No. 7, 1976, pp. 2178-2180. Zbl0329.22013MR57 #538
  12. [12] R. LANGLANDS, On the Classification of Irreducible Representations of Real Algebraic Groups, mimeographed notes, Inst. for Adv. Study, 1973. 
  13. [13] G. I. OLSHANSKY, Intertwining Operators and Complementary Series in the Class of Representations of the General Group of Matrices Over a Locally Compact Division Algebra, Induced from Parabolic Subgroups (Mat. Sb., Vol. 93, No. 2, 1974, pp. 218-253). 
  14. [14] A. V. ZELEVINSKY, Classification of Irreducible Non-Cuspidal Representations of the Group GLn Over a p-Adic Field (Funkc. Anal. i Priložen, Vol. 11, No. 1, 1977, pp. 67-68). Zbl0363.22012
  15. [15] A. V. ZELEVINSKY, The Representation Ring of Groups GL(n) Over a p-Adic Field (Funkc. Anal. i Priložen, Vol. 11, No. 3, 1977, pp. 78-79). 

Citations in EuDML Documents

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  1. Chris Jantzen, Reducibility of certain representations for symplectic and odd-orthogonal groups
  2. Christophe Breuil, [unknown]
  3. J.-L. Waldspurger, Un exercice sur G S p ( 4 , F ) et les représentations de Weil
  4. François Courtès, Sur le transfert des intégrales orbitales pour les groupes linéaires (cas p -adique)
  5. Laurent Clozel, Sur une conjecture de Howe. I
  6. Colin J. Bushnell, Guy Henniart, Local tame lifting for G L ( N ) . I: Simple characters
  7. Guy Henniart, Induction automorphe globale pour les corps de nombres
  8. Guy Henniart, Une caractérisation de la correspondance de Langlands locale pour GL ( n )
  9. Marko Tadic, Spherical unitary dual of general linear group over non-Archimidean local field
  10. Alexandru Ioan Badulescu, Correspondance de Jacquet–Langlands pour les corps locaux de caractéristique non nulle

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