Unipotent automorphic representations : conjectures

Arthur, James

Orbites unipotentes et représentations - II. Groupes

p

-adiques et réels, Astérisque, no. 171-172 (1989), pp. 13-71

MR Zbl | 12 citations dans Numdam

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     author = {Arthur, James},
     title = {Unipotent automorphic representations : conjectures},
     booktitle = {Orbites unipotentes et repr\'esentations - II. Groupes $p$-adiques et r\'eels},
     series = {Ast\'erisque},
     pages = {13--71},
     year = {1989},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {171-172},
     mrnumber = {1021499},
     zbl = {0728.22014},
     language = {en},
     url = {https://www.numdam.org/item/AST_1989__171-172__13_0/}
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Arthur, James. Unipotent automorphic representations : conjectures, dans Orbites unipotentes et représentations - II. Groupes $p$-adiques et réels, Astérisque, no. 171-172 (1989), pp. 13-71. https://www.numdam.org/item/AST_1989__171-172__13_0/

Bibliographie
Cité par

1. J. Adams and J. Johnson, Endoscopic groups and packets of non-tempered representations, Compositio Math. 64 (1987), 271-309. | MR | Zbl | EuDML | Numdam

2. J. Arthur, On some problems suggested by the trace formula, in Lie Group Representations II Lecture Notes in Math., vol. 1041, Springer-Verlag, 1983, pp. 1-49. | MR | Zbl | DOI

3. J. Arthur, The local behaviour of weighted orbital integrals, Duke J. Math. 56 (1988), 223-293. | MR | Zbl | DOI

4. J. Arthur, Intertwining operators and residues I. Weighted characters, to appear in J. Funct. Anal. | MR | Zbl

5. J. Arthur, Unipotent automorphic representations. Global motivation, in preparation. | Zbl

6. J. Arthur and L. Clozel, Simple Algebras, Base Change and the Advanced Theory of the Trace Formula, to appear in Annals of Math. Studies, Princeton Univ. Press. | MR | Zbl

7. D. Barbasch and D. Vogan, Unipotent representations of complex semisimple Lie groups, Ann. of Math. 121 (1985), 41-110. | Zbl | MR | DOI

8. A. Borel, Automorphic $L$ -functions, in Automorphic Forms, Representations and $L$ -functions, Proc. Sympos. Pure Math. 33, Part II, A.M.S., Providence, 1979, pp. 27-62. | MR | Zbl

9. A. Borel and W. Casselman, $L^{2}$ -cohomology of locally symmetric manifolds of finite volume, Duke Math. J. 50 (1983), 625-647. | MR | Zbl | DOI

10. A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups and Representations of Reductive Groups, Annals of Math. Studies, 94, Princeton Univ. Press, 1980. | MR | Zbl

11. D. Flath, Decomposition of representations into tensor products, in Automorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math. 33, Part I, A.M.S., Providence, 1979, pp. 179-184. | MR | Zbl | DOI

12. A. Fröhlich and J. Queyrut, On the functional equations of the Artin $L$ -function for characters of real representations, Invent. Math. 20 (1973), 125-138. | MR | Zbl | EuDML | DOI

13. Harish-Chandra, Discrete series for semisimple Lie groups II, Acta. Math. 116 (1966), 1-111. | Zbl | DOI

14. Harish-Chandra, Harmonic analysis on $p$ -adic groups, in Harmonic Analysis on Homogeneous Spaces, Proc. Sympos. Pure Math. 26, A.M.S. Providence, 1973, pp. 167-192. | Zbl | MR | DOI

15. R. Howe and I. Piatetskii-Shapiro, A counterexample to the "generalized Ramanujan conjecture" for (quasi-)split groups, in Automorphic Forms, Representations and $L$ -functions, Proc. Sympos. Pure Math. 33, Part I, A.M.S., Providence, 1979, pp. 315-322. | Zbl | MR | DOI

16. H. Jacquet, On the residual spectrum of $G L (n)$ , in Lie Group Representations II, Lecture Notes in Math., vol. 1041, Springer-Verlag, 1983, pp. 1-49. | Zbl | MR

17. D. Keys, $L$ -indistinguishability and $R$ -groups for quasi-split groups: unitary groups in even dimension, Ann. Scient. Ec. Norm. Sup., 4e serie, t. 31 (1987), 31-64. | MR | Zbl | Numdam | EuDML | DOI

18. D. Keys and F. Shahidi, Artin $L$ -functions and normalization of intertwining operators, to appear in Ann. Scient. Ec. Norm. Sup. | MR | Zbl | EuDML | Numdam

19. A. Knapp and G. Zuckerman, Normalizing factors, tempered representations, and $L$ -groups, in Autormorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math. 33, Part I, A.M.S., Providence, 1979, pp. 93-106. | MR | Zbl | DOI

20. R. Kottwitz, Sign changes in harmonic analysis on reductive groups, Trans. Amer. Math. Soc. 278 (1983), 289-297. | MR | Zbl | DOI

21. R. Kottwitz, Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), 611-650. | MR | Zbl | DOI

22. R. Kottwitz, Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), 365-399. | MR | Zbl | EuDML | DOI

23. N. Kurokawa, Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two, Invent. Math. 49 (1978), 149-165. | MR | Zbl | EuDML | DOI

24. J.-P. Labesse and R. Langlands, $L$ -indistinguishability for $S L (2)$ , Canad. J. Math. 31 (1979), 726-785. | MR | Zbl | DOI

25. R. Langlands, Problems in the theory of automorphic forms, in Lectures in Modern Analysis and Applications, Lecture Notes in Math., vol 170, Springer-Verlag, 1970, pp. 18-86. | MR | Zbl

26. R. Langlands, On Artin's $L$ -function, Rice University Studies 56 (1970), 23-28. | Zbl

27. R. Langlands, On the classification of irreducible representations of real reductive groups, to appear in Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Math. Surveys and Monographs, 30, A.M.S., Providence. | MR | Zbl

28. R. Langlands, On the Functional Equations Satisfied by Eisenstein Series, Lecture Notes in Math., vol. 544, Springer-Verlag, 1976. | MR | Zbl

29. R. Langlands, Automorphic representations, Shimura varieties and motives. Ein Märchen, in Automorphic Forms, Representations and $L$ -functions, Proc. Sympos. Pure Math. 33, Part II, A.M.S., Providence, 1979, pp. 205-246. | MR | Zbl | DOI

30. R. Langlands, Stable conjugacy: definitions and lemmas, Canad. J. Math. 31 (1979), 700-725. | MR | Zbl | DOI

31. R. Langlands, On the zeta functions of some simple Shimura varieties, Canad. J. Math. 31 (1979), 1121-1216. | MR | Zbl | DOI

32. R. Langlands, Les Débuts d'une Formule des Traces Stable, Publ. Math. Univ. Paris VII, Vol. 13, Paris (1983). | MR | Zbl

33. R. Langlands and D. Shelstad, On the definition of transfer factors, Math. Ann. 278 (1987), 219-271. | MR | Zbl | EuDML | DOI

34. J. Rogawski, Automorphic Representations of Unitary Groups in Three Variables, to appear in Annals of Math. Studies, Princeton Univ. Press. | MR | Zbl

35. F. Shahidi, Local coefficients and normalization of intertwining opertors for $G L (n)$ , Compositio Math. 48 (1983), 271-295. | MR | Zbl | EuDML | Numdam

36. F. Shahidi, Some results on L-indistinguishability for $S L (r)$ , Canad. J. Math. 35 (1983), 1075-1109. | MR | Zbl | DOI

37. F. Shahidi, Local coefficients as Artin factors for real groups, Duke Math. J. 52 (1985), 973-1007. | MR | Zbl | DOI

38. D. Shelstad, Notes on $L$ -indistinguishability (based on a lecture by R.P. Langlands), in Automorphic Forms, Representations and $L$ -functions, Proc. Sympos. Pure Math. 33, Part II, A.M.S., Providence, 1979, pp. 193-204. | MR | Zbl | DOI

39. D. Shelstad, Orbital integrals and a family of groups attached to a real reductive group, Ann. Scient. Éc. Norm. Sup., 4e serie, t. 12 (1979), 1-31. | MR | Zbl | EuDML | Numdam | DOI

40. D. Shelstad, Embeddings of $L$ -groups, Canad. J. Math., 33 (1981), 513-558. | MR | Zbl | DOI

41. D. Shelstad, $L$ -indistinguishability for real groups, Math. Ann. 259 (1982), 385-430. | MR | Zbl | EuDML | DOI

42. B. Speh, Unitary representations of $S L (n, ℝ)$ and the cohomology of congruence subgroups, in Non-commutative Harmonic Analysis and Lie Groups, Lecture Notes in Math., vol. 880, Springer-Verlag, 1981, pp. 483-505. | MR | Zbl | DOI

43. T. Springer, Linear Algebraic Groups, Prog. Math. 9, 1981, Birkhäuser. | MR | Zbl

44. R. Steinberg, Endomorphisms of Linear Algebraic Groups, Mem. Amer. Math. Soc. 80. 1968. | MR | Zbl

45. M. Tadic, Classification of unitary representations in irreducible representations of general linear group (non-archimedean case), Ann. Scient. Ec. Norm. Sup., 4e serie, t. 19 (1986), 335-382. | MR | Zbl | EuDML | Numdam | DOI

M. Tadic, Classification of unitary representations in irreducible representations of general linear group (non-archimedean case), Ann. Scient. Ec. Norm. Sup., 4e serie, t. 13 (1985), 39-42. | Numdam | EuDML | MR | Zbl

46. J. Tate, Number theoretic background, in Automorphic Forms, Representations and $L$ -functions, Proc. Sympos. Pure Math. 33, Part II, A.M.S., Providence, 1979, pp. 3-26. | Zbl | MR | DOI

47. D. Vogan, Representations of Real Reductive Lie Groups, Prog. Math. 15, 1981, Birkhäuser. | MR | Zbl

48. D. Vogan, Unitarizability of certain series of representations, Ann. of Math. 120 (1984), 141-187. | MR | Zbl | DOI

49. D. Vogan, The unitary dual of $G L (n)$ over an archimedean field, Invent. Math. 83 (1986), 449-505. | MR | Zbl | EuDML | DOI

50. D. Vogan, Representations of reductive Lie groups, Proceedings of the International Congress of Mathematicians, Berkeley, 1986, Vol. 1, 245-266. | MR | Zbl

51. D. Vogan, Unitary Representations of Reductive Lie Groups, to appear in Annals of Math. Studies, Princeton Univ. Press. | MR | Zbl

52. D. Vogan and G. Zuckerman, Unitary representations with non-zero cohomology, Compositio Math. 53 (1984), 51-90. | MR | Zbl | EuDML | Numdam