Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 19 (1986) no. 3, p. 335-382
@article{ASENS_1986_4_19_3_335_0,
     author = {Tadi\'c, Marko},
     title = {Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 19},
     number = {3},
     year = {1986},
     pages = {335-382},
     doi = {10.24033/asens.1510},
     zbl = {0614.22005},
     mrnumber = {88b:22021},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1986_4_19_3_335_0}
}
Tadić, Marko. Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case). Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 19 (1986) no. 3, pp. 335-382. doi : 10.24033/asens.1510. http://www.numdam.org/item/ASENS_1986_4_19_3_335_0/

[1] J. N. Bernstein, All Reductive p-adic Groups Are Tame (Funct. Anal. Appl., Vol. 8, 1974, pp. 91-93). | MR 50 #543 | Zbl 0298.43013

[2] J. N. Bernstein, P-Invariant Distributions on GL (N) and the Classification of Unitary Representations of GL (N) (Non-Archimedean Case), in Lie Group Representations II (Proceedings, University of Maryland, 1982-1983, Lecture Notes in Math., Vol. 1041, Springer-Verlag, Berlin, 1984, pp. 50-102). | Zbl 0541.22009

[3] J. N. Bernstein, P. Deligne, D. Kazhdan and M. F. Vigneras, Représentations des groupes réductifs sur un corps local, Hermann, Paris, 1984. | Zbl 0544.00007

[4] J. 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 (= Russian Math. Surveys, Vol. 31, No. 3, 1976, pp. 1-68)]. | Zbl 0348.43007

[5] J. N. Bernstein and A. V. Zelevinsky, Induced Representations of Reductive p-adic Groups, I (Ann. Scient. Éc. Norm. Sup., Vol. 10, 1977, pp. 441-472). | Numdam | MR 58 #28310 | Zbl 0412.22015

[6] P. Cartier, Representations of p-adic Groups : a Survey, in Proc. Sympos. Pure Math., Vol. XXXIII, part 1, Amer. Math. Soc., Providence, R. I., 1979, pp. 111-155. | MR 81e:22029 | Zbl 0421.22010

[7] W. Casselman, Introduction to the Theory of Admissible Representations of p-adic Reductive Groups, preprint.

[8] G. Van Dijk, Computation of Certain Induced Characters of p-adic Groups (Math. Ann., Vol. 199, 1972, pp. 229-240). | MR 49 #3043 | Zbl 0231.22018

[9] D. Flath, Decomposition of Representations into Tensor Products, in Proc. Sympos. Pure Math., Vol. XXXIII, part I, Amer. Math. Soc., Providence, R. I., 1979, pp. 179-183. | MR 81f:22028 | Zbl 0414.22019

[10] I. M. Gelfand and M. I. Graev, Representations of a Group of the Second Order with Elements from a Locally Compact Field (Russian Math. Surveys, Vol. 18, 1963, pp. 29-100). | MR 27 #5864 | Zbl 0166.40201

[11] I. M. Gelfand, M. Graev and I. I. Piatetski-Shapiro, Automorphic Functions and Representation Theory, W. B. Sannders Co., Philadelphia, 1969. | Zbl 0177.18003

[12] I. M. Gelfand and D. A. Kazhdan, Representations of GL (n, K), in Lie Groups and Their Representations, Akademiai Kiado, Budapest, 1974, pp. 95-118. | Zbl 0348.22011

[13] I. M. Gelfand and M. A. Neumark, Unitare Darstellungen der Klassichen Gruppen, German translation, Akademie Verlag, Berlin, 1957. | Zbl 0077.03405

[14] H. Jacquet, Generic Representations, in Non-Commutative Harmonic Analysis (Lecture Notes in Math., Vol. 587, Springer-Verlag, Berlin, 1977, pp. 91-101). | MR 58 #16985 | Zbl 0357.22010

[15] H. Jacquet, Principal L-functions of the linear group, in Proc. Sympos. Pure Math., Vol. XXXIII, part 2, Amer. Math. Soc., Providence, R. I., 1979, pp. 63-86. | MR 81f:22029 | Zbl 0413.12007

[16] H. Jacquet, On the Residual Spectrum of GL(n), in Lie Group Representations II (Proceedings, University of Maryland, 1982-1983, Lecture Notes in Math., Vol. 1041, Springer-Verlag, Berlin, 1984, pp. 185-208). | MR 85k:22045 | Zbl 0539.22016

[17] A. Knapp and B. Speh, Status of Classification of Irreducible Unitary Representations, in Harmonic Analysis (Proceedings, Minneapolis, 1981, Lecture Notes in Math., Vol. 908, Springer-Verlag, Berlin, 1982). | Zbl 0496.22018

[18] D. Miličić, On C*-Algebras with Bounded Trace (Glasnik Mat., Vol. 8, (28), 1973, pp. 7-22). | MR 48 #2781 | Zbl 0265.46072

[19] C. Moeglin and J.-L. Waldspurger, Sur l'involution de Zelevinsky, preprint, Paris, 1985.

[20] 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).

[21] F. Rodier, Représentations de GL (n, k) où k est un corps p-adique [Séminaire Bourbaki, n° 587, 1982, (Astérisque, 92-93, 1982, pp. 201-218)]. | Numdam | MR 84h:22040 | Zbl 0506.22019

[22] J. Rogawski, Representations of GL (n) and Division Algebras Over a p-adic Field (Duke Math. J., Vol. 50, 1983, pp. 161-196). | MR 84j:12018 | Zbl 0523.22015

[23] B. Speh, The Unitary Dual of GL (3, ℝ) and GL (4, ℝ) (Math. Ann., Vol. 258, 1981, pp. 113-133). | MR 83i:22025 | Zbl 0483.22005

[24] B. Speh, Unitary Representations of GL (n, ℝ) with Non-Trivial (g, K) Cohomology (Invent. Math., Vol. 71, 1983, pp. 443-465). | MR 84k:22024 | Zbl 0505.22015

[25] E. M. Stein, Analysis in Matrix Spaces and Some New Representations of SL (N, ℂ) (Ann. of Math., Vol. 86, 1967, pp. 461-490). | MR 36 #2749 | Zbl 0188.45303

[26] M. Tadić, The C*-algebra of SL (2, k) (Glasnik Mat., Vol. 17, (37), 1982, pp. 249-263). | MR 84g:22038 | Zbl 0504.22014

[27] M. Tadić, The Topology of the Dual Space of a Reductive Group Over a Local Field (Glasnik Mat., 18, (38), 1983, pp. 259-279). | MR 85k:22043 | Zbl 0536.22026

[28] M. Tadić, Proof of a Conjecture of Bernstein, (Math. Ann., Vol. 272, 1985, pp. 11-16). | MR 87i:22049 | Zbl 0547.22010

[29] M. Tadić, Unitary Dual of p-Adic GL (n). Proof of Bernstein Conjectures, (Bull. Amer. Math. Soc., Vol. 13, No. 1, 1985, pp. 39-42). | MR 86j:22029 | Zbl 0583.22008

[30] M. Tadić, Unitary Representations of General Linear Group Over Real and Complex Field, preprint, Bonn, 1985.

[31] D. A. Vogan, Jr., Understanding the Unitary Dual, in Lie Group Representations I (Proceedings, University of Maryland, 1982-1983, Lecture Notes in Math., Vol. 1024, Springer-Verlag, Berlin 1983, pp. 264-286). | MR 86b:22027 | Zbl 0527.22017

[32] N. R. Wallach, Representations of Reductive Lie Groups, in Proc. Sympos. Pure Math., Vol. XXXIII, part 1, Amer. Math. Soc., Providence, R. I., 1979, pp. 71-86). | MR 80m:22024 | Zbl 0421.22006

[33] A. V. Zelevinsky, Induced representations of reductive p-adic groups II (Ann. Scient. Éc. Norm. Sup., Vol. 13, 1980, pp. 165-210). | Numdam | MR 83g:22012 | Zbl 0441.22014

[34] A. V. Zelevinsky, p-adic analogue of the Kazhdan-Lusztig conjecture (Funct. Anal. Appl., Vol. 15, 1981, pp. 83-92). | MR 84g:22039 | Zbl 0476.22014

[35] J.-L. Waldspurger, Algèbres de Hecke et induites de représentations cuspidales, pour GL (N) (Journal für die Reine und angewandte Matematik, No. 370, 1986, pp. 127-191). | MR 87m:22048 | Zbl 0586.20020