Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)

 Access to full text

 Full (PDF)

1. [1] J. N. BERNSTEIN, All Reductive p-adic Groups Are Tame (Funct. Anal. Appl., Vol. 8, 1974, pp. 91-93). Zbl0298.43013MR50 #543
2. [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). Zbl0541.22009
3. [3] J. N. BERNSTEIN, P. DELIGNE, D. KAZHDAN and M. F. VIGNERAS, Représentations des groupes réductifs sur un corps local, Hermann, Paris, 1984. Zbl0544.00007
4. [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)]. Zbl0348.43007
5. [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). Zbl0412.22015MR58 #28310
6. [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. Zbl0421.22010MR81e:22029
7. [7] W. CASSELMAN, Introduction to the Theory of Admissible Representations of p-adic Reductive Groups, preprint. 
8. [8] G. VAN DIJK, Computation of Certain Induced Characters of p-adic Groups (Math. Ann., Vol. 199, 1972, pp. 229-240). Zbl0231.22018MR49 #3043
9. [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. Zbl0414.22019MR81f:22028
10. [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). Zbl0166.40201MR27 #5864
11. [11] I. M. GELFAND, M. GRAEV and I. I. PIATETSKI-SHAPIRO, Automorphic Functions and Representation Theory, W. B. Sannders Co., Philadelphia, 1969. Zbl0177.18003
12. [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. Zbl0348.22011
13. [13] I. M. GELFAND and M. A. NEUMARK, Unitare Darstellungen der Klassichen Gruppen, German translation, Akademie Verlag, Berlin, 1957. Zbl0077.03405
14. [14] H. JACQUET, Generic Representations, in Non-Commutative Harmonic Analysis (Lecture Notes in Math., Vol. 587, Springer-Verlag, Berlin, 1977, pp. 91-101). Zbl0357.22010MR58 #16985
15. [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. Zbl0413.12007MR81f:22029
16. [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). Zbl0539.22016MR85k:22045
17. [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). Zbl0496.22018
18. [18] D. MILIČIĆ, On C*-Algebras with Bounded Trace (Glasnik Mat., Vol. 8, (28), 1973, pp. 7-22). Zbl0265.46072MR48 #2781
19. [19] C. MOEGLIN and J.-L. WALDSPURGER, Sur l'involution de Zelevinsky, preprint, Paris, 1985. 
20. [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. [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)]. Zbl0506.22019MR84h:22040
22. [22] J. ROGAWSKI, Representations of GL (n) and Division Algebras Over a p-adic Field (Duke Math. J., Vol. 50, 1983, pp. 161-196). Zbl0523.22015MR84j:12018
23. [23] B. SPEH, The Unitary Dual of GL (3, ℝ) and GL (4, ℝ) (Math. Ann., Vol. 258, 1981, pp. 113-133). Zbl0483.22005MR83i:22025
24. [24] B. SPEH, Unitary Representations of GL (n, ℝ) with Non-Trivial (g, K) Cohomology (Invent. Math., Vol. 71, 1983, pp. 443-465). Zbl0505.22015MR84k:22024
25. [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). Zbl0188.45303MR36 #2749
26. [26] M. TADIĆ, The C*-algebra of SL (2, k) (Glasnik Mat., Vol. 17, (37), 1982, pp. 249-263). Zbl0504.22014MR84g:22038
27. [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). Zbl0536.22026MR85k:22043
28. [28] M. TADIĆ, Proof of a Conjecture of Bernstein, (Math. Ann., Vol. 272, 1985, pp. 11-16). Zbl0547.22010MR87i:22049
29. [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). Zbl0583.22008MR86j:22029
30. [30] M. TADIĆ, Unitary Representations of General Linear Group Over Real and Complex Field, preprint, Bonn, 1985. 
31. [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). Zbl0527.22017MR86b:22027
32. [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). Zbl0421.22006MR80m:22024
33. [33] A. V. ZELEVINSKY, Induced representations of reductive p-adic groups II (Ann. Scient. Éc. Norm. Sup., Vol. 13, 1980, pp. 165-210). Zbl0441.22014MR83g:22012
34. [34] A. V. ZELEVINSKY, p-adic analogue of the Kazhdan-Lusztig conjecture (Funct. Anal. Appl., Vol. 15, 1981, pp. 83-92). Zbl0476.22014MR84g:22039
35. [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). Zbl0586.20020MR87m:22048

1. Siddhartha Sahi, On Kirillov's conjecture for archimedean fields
2. Guy Henniart, Induction automorphe globale pour les corps de nombres
3. Marko Tadic, Spherical unitary dual of general linear group over non-Archimidean local field
4. Paul J.jun. Sally, Marko Tadic, Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$
5. François Rodier, Sur les représentations non ramifiées des groupes réductifs $p$-adiques ; l’exemple de $GSp\left(4\right)$
6. Marko Tadić, Representations of $p$-adic symplectic groups
7. Laurent Clozel, Progrès récents vers la classification du dual unitaire des groupes réductifs réels
8. Yuval Z. Flicker, Distinguished representations and a Fourier summation formula
9. C. Mœglin, J.-L. Waldspurger, Le spectre résiduel de $\mathrm{GL}\left(n\right)$
10. Dubravka Ban, The Aubert involution and R-groups