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Zelevinsky, A. V.

Induced representations of reductive \(p\)-adic groups. II: On irreducible representations of \(GL(n)\). (English) Zbl 0441.22014

Ann. Sci. Éc. Norm. Supér. (4) 13, 165-210 (1980).
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Cited in 30 Reviews
Cited in 338 Documents

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields

Keywords:

p-adic field; general linear group; bialgebra structure; cuspidal irreducible representation; Whittaker models

Citations:

Zbl 0412.22015
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\textit{A. V. Zelevinsky}, Ann. Sci. Éc. Norm. Supér. (4) 13, 165--210 (1980; Zbl 0441.22014)
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References:

[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). Numdam | MR 58 #28310 | Zbl 0412.22015 · Zbl 0412.22015
[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). MR 54 #12988 | Zbl 0348.43007 · Zbl 0348.43007
[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). MR 54 #12989
[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). MR 45 #298 | Zbl 0246.17008 · Zbl 0246.17008
[5] N. BOURBAKI , Algèbre , Chap. 1 à 3, Hermann, Paris, 1970 . Zbl 0211.02401 · Zbl 0211.02401
[6] W. CASSELMAN , Introduction to the Theory of Admissible Representations of p-Adic Reductive Groups , preprint.
[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 ). MR 50 #240 | Zbl 0271.10032 · Zbl 0271.10032
[8] I. M. GELFAND and D. A. KAZHDAN , Representations of GL (n, K) , in Lie Groups and Their Representations, Akadèmiai Kiado, Budapest, 1974 . · Zbl 0348.22011
[9] R. GODEMENT and H. JACQUET , Zeta-Functions of Simple Algebras (Lecture Notes in Math., 260, Springer-Verlag, 1972 ). MR 49 #7241 | Zbl 0244.12011 · Zbl 0244.12011
[10] M. HALL , Combinatorial Theory , Blaisdell Publ. Comp., 1967 . MR 37 #80 | Zbl 0196.02401 · Zbl 0196.02401
[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. MR 57 #538 | Zbl 0329.22013 · Zbl 0329.22013
[12] R. LANGLANDS , On the Classification of Irreducible Representations of Real Algebraic Groups , mimeographed notes, Inst. for Adv. Study, 1973 . · Zbl 0741.22009
[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). · Zbl 0298.22016
[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). Zbl 0363.22012 · Zbl 0363.22012
[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).
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