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Induced representations of reductive \(p\)-adic groups. I. (English) Zbl 0412.22015


MSC:

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

Citations:

Zbl 0289.22017
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References:

[1] 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). Zbl 0348.43007 · Zbl 0348.43007
[2] I. N. BERNSTEIN and A. V. ZELEVINSKY , Induced Representations of the Group GL (n) over a p-adic Field (Funkt. Anal. i Priložen., Vol. 10, No. 3, 1976 , pp. 74-75). MR 54 #12989
[3] A. BOREL , Linear Algebraic Groups , Benjamin, New York-Amsterdam, 1969 . MR 40 #4273 | Zbl 0186.33201 · Zbl 0186.33201
[4] A. BOREL et J. TITS , Groupes réductifs (Publ. Math. I.H.E.S., No. 27, 1965 ). Numdam | MR 34 #7527 | Zbl 0145.17402 · Zbl 0145.17402
[5] N. BOURBAKI , Groupes et algèbres de Lie , Chap. 4, 5 et 6, Hermann Paris, 1968 . Zbl 0186.33001 · Zbl 0186.33001
[6] W. CASSELMAN , Steinberg Character as a True Character (Proc. Sympos. Pure Math., Vol. 26, 1972 , pp. 413-418). MR 49 #3039 | Zbl 0289.22017 · Zbl 0289.22017
[7] G. VAN DIJK , Some Recent Results of Harish-Chandra for p-adic groups [Colloque sur les fonctions sphériques, Nancy, 5-9 janvier 1971 (preprint)]. MR 55 #12879 | Zbl 0352.22016 · Zbl 0352.22016
[8] I. M. GELFAND and D. A. KAJDAN , On Representations of the Group GL (n, K), where K is a local Field (Funkt. Anal. i Priložen., Vol. 6, No. 4, 1972 , pp. 73-74).
[9] I. M. GELFAND and D. A. KAJDAN , Representations of GL (n, K) , in “Lie Groups and their Representations 2, Akadèmiai Kiado, Budapest, 1974 .
[10] H. JACQUET , Sur les représentations des groupes réductifs p-adiques (C. R. Acad. Sc. Paris, t. 280, No. 19, série A, 1975 , pp. 1271-1272. MR 51 #5856 | Zbl 0309.22012 · Zbl 0309.22012
[11] HARISH-CHANDRA , Harmonic Analysis on Reductive p-adic Groups (preprint). · Zbl 0289.22018
[12] R. HOWE , Some Qualitative Results on the Representation Theory of GLn over a p-adic Field (Inst. for Adv. Study 1972 ).
[13] D. M. KAN , Adjoint Functors (Trans. Amer. Math. Soc., Vol. 87, 1958 , pp. 294-329). MR 24 #A1301 | Zbl 0090.38906 · Zbl 0090.38906
[14] 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 · Zbl 0298.22016
[15] T. A. SPRINGER , Cusp Forms for Finite Groups , in Seminar on Algebraic Groups and Related Finite Groups, (Lecture Notes in Math., Vol. 131, Springer-Verlag, 1970 ). MR 41 #8541 | Zbl 0263.20024 · Zbl 0263.20024
[16] R. STEINBERG , Lectures on Chevalley Groups , Yale University, 1967 . · Zbl 0164.34302
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