Induced representations of reductive 𝔭 -adic groups. I

I. N. Bernstein; A. V. Zelevinsky

Annales scientifiques de l'École Normale Supérieure (1977)

  • Volume: 10, Issue: 4, page 441-472
  • ISSN: 0012-9593

How to cite

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Bernstein, I. N., and Zelevinsky, A. V.. "Induced representations of reductive ${\mathfrak {p}}$-adic groups. I." Annales scientifiques de l'École Normale Supérieure 10.4 (1977): 441-472. <http://eudml.org/doc/82002>.

@article{Bernstein1977,
author = {Bernstein, I. N., Zelevinsky, A. V.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {reductive p-adic groups; connected algebraic group; irreducible representation; Levi component; Kirillov model; Lie group},
language = {eng},
number = {4},
pages = {441-472},
publisher = {Elsevier},
title = {Induced representations of reductive $\{\mathfrak \{p\}\}$-adic groups. I},
url = {http://eudml.org/doc/82002},
volume = {10},
year = {1977},
}

TY - JOUR
AU - Bernstein, I. N.
AU - Zelevinsky, A. V.
TI - Induced representations of reductive ${\mathfrak {p}}$-adic groups. I
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1977
PB - Elsevier
VL - 10
IS - 4
SP - 441
EP - 472
LA - eng
KW - reductive p-adic groups; connected algebraic group; irreducible representation; Levi component; Kirillov model; Lie group
UR - http://eudml.org/doc/82002
ER -

References

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  1. [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). Zbl0348.43007
  2. [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). MR54 #12989
  3. [3] A. BOREL, Linear Algebraic Groups, Benjamin, New York-Amsterdam, 1969. Zbl0186.33201MR40 #4273
  4. [4] A. BOREL et J. TITS, Groupes réductifs (Publ. Math. I.H.E.S., No. 27, 1965). Zbl0145.17402MR34 #7527
  5. [5] N. BOURBAKI, Groupes et algèbres de Lie, Chap. 4, 5 et 6, Hermann Paris, 1968. Zbl0186.33001
  6. [6] W. CASSELMAN, Steinberg Character as a True Character (Proc. Sympos. Pure Math., Vol. 26, 1972, pp. 413-418). Zbl0289.22017MR49 #3039
  7. [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)]. Zbl0352.22016MR55 #12879
  8. [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. [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. [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. Zbl0309.22012MR51 #5856
  11. [11] HARISH-CHANDRA, Harmonic Analysis on Reductive p-adic Groups (preprint). 
  12. [12] R. HOWE, Some Qualitative Results on the Representation Theory of GLn over a p-adic Field (Inst. for Adv. Study 1972). 
  13. [13] D. M. KAN, Adjoint Functors (Trans. Amer. Math. Soc., Vol. 87, 1958, pp. 294-329). Zbl0090.38906MR24 #A1301
  14. [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). Zbl0298.22016
  15. [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). Zbl0263.20024MR41 #8541
  16. [16] R. STEINBERG, Lectures on Chevalley Groups, Yale University, 1967. 

Citations in EuDML Documents

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  1. A. V. Zelevinsky, Induced representations of reductive 𝔭 -adic groups. II. On irreducible representations of GL ( n )
  2. L. Clozel, Théorème d’Atiyah-Bott pour les variétés 𝔭 -adiques et caractères des groupes réductifs
  3. Rebecca A. Herb, Supertempered virtual characters
  4. Siddhartha Sahi, On Kirillov's conjecture for archimedean fields
  5. Freydoon Shahidi, Local coefficients and normalization of intertwining operators for G L ( n )
  6. S. J. Patterson, Metaplectic forms and Gauss sums I
  7. Laurent Clozel, Sur une conjecture de Howe. I
  8. Paul J.jun. Sally, Marko Tadic, Induced representations and classification for G S p ( 2 , F ) and S p ( 2 , F )
  9. Yuval Z. Flicker, On endo-lifting
  10. Yuval Z. Flicker, Twisted tensors and Euler products

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