Clozel, Laurent Changement de base pour les représentations temperees des groupes reductifs réels. (French) Zbl 0516.22010 Ann. Sci. Éc. Norm. Supér. (4) 15, 45-115 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 20 Documents MSC: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods Keywords:change of basis; integrability; discrete series; tempered distribution; tempered representation; lifting; reductive group; irreducible admissible representations; L-group; L-packet; tempered L-packets Citations:Zbl 0342.20021 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] A. BOREL , Automorphic L-Functions (Proc. Sym. Pure Math., vol. 33, n^\circ 2, 1979 , p. 27-61). MR 81m:10056 | Zbl 0412.10017 · Zbl 0412.10017 [2] A. BOREL et J. TITS , Groupes réductifs (I.H.E.S. Publ. Math., vol. 27, 1975 , p. 55-150). Numdam | MR 34 #7527 | Zbl 0145.17402 · Zbl 0145.17402 · doi:10.1007/BF02684375 [3] A. BOREL et N. WALLACH , Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (Ann. of Math. Studies, vol. 94, Princeton U.P. 1980 ). MR 83c:22018 | Zbl 0443.22010 · Zbl 0443.22010 [4] L. CLOZEL , ”Base Change” géométrique: Relèvement de la série principale de GL (n, \Bbb C/\Bbb R) , Springer LN 728, 1979 , p. 17-41. MR 81d:20038 | Zbl 0495.20020 · Zbl 0495.20020 · doi:10.1007/BFb0063336 [5] L. CLOZEL , Sur le ”base change” pour les formes réelles de GL (2, \Bbb C) , Université Paris-VII, U.E.R. de Math., 1980 . [6] M. DUFLO , Représentations irréductibles des groupes semi-simples complexes , Springer LN 497, 1975 , p. 26-88. MR 53 #3198 | Zbl 0315.22008 · Zbl 0315.22008 [7] P. GERARDIN , La classification de R.P. Langlands des représentations irréductibles des groupes réductifs réels (notes non publiées). [8] S. HELGASON , Differential Geometry and Symmetric Spaces , Academic Press, 1959 . · Zbl 0146.43601 [9] T. HIRAI , The Characters of Some Induced Representations of Semi-Simple Lie Groups (J. Math. Kyoto Univ., vol. 8, 1968 , p. 313-363). Article | MR 39 #354 | Zbl 0185.21503 · Zbl 0185.21503 [10] A. KNAPP , Commutativity of Intertwining Operators II (Bull. A. M. S. vol. 82, 1976 , p. 271-273). Article | MR 53 #10986 | Zbl 0333.22006 · Zbl 0333.22006 · doi:10.1090/S0002-9904-1976-14019-0 [11] A. KNAPP , Commutativity of Intertwining Operators for Semi-Simple Groups (preprint). · Zbl 0488.22027 [12] A. KNAPP et E. M. STEIN , Intertwining Operators for Semi-Simple Groups (Ann. of Math., vol. 93, 1971 , p. 489-578). MR 57 #536 | Zbl 0257.22015 · Zbl 0257.22015 · doi:10.2307/1970887 [13] R. P. LANGLANDS , Problems in the Theory of Automorphic Forms , Springer LN 170, 1970 , p. 18-86. MR 46 #1758 | Zbl 0225.14022 · Zbl 0225.14022 [14] R. P. LANGLANDS , On the Classification of Irreducible Representations of Real Algebraic Groups , preprint (sic), I.A.S., Princeton, 1973 . · Zbl 0741.22009 [15] R. P. LANGLANDS , Stable Conjugacy: Definitions and Lemmas (Can. J. Math., vol. 31, n^\circ 4, 1979 , p. 700-725). MR 82j:10054 | Zbl 0421.12013 · Zbl 0421.12013 · doi:10.4153/CJM-1979-069-2 [16] J. REPKA , Base Change Lifting and Galois Invariance (preprint). · Zbl 0431.12015 [17] J. REPKA , Base Change for Tempered Irreductible Representations of GL (n, \Bbb R) (à paraître). · Zbl 0443.22011 [18] J. REPKA , Base Change and Induced Representations of Real Reductive Groups (preprint). [19] D. SHELSTAD , Characters and Inner Forms of a Quasi-Split Group Over \Bbb R , (Comp. Math., vol. 39, 1979 , p. 11-45). Numdam | MR 80m:22023 | Zbl 0431.22011 · Zbl 0431.22011 [20] D. SHELSTAD , Some Character Relations for Real Reductive Algebraic Groups (Thèse, Yale, 1974 ). [21] D. SHELSTAD , Base Change and a Matching Theorem for Real Groups (preprint). · Zbl 0494.22007 [22] T. SHINTANI , On Irreductible Unitary Characters of a Certain Group Extention of GL (2, \Bbb C) (J. Math. Soc. Japan, vol. 29, n^\circ 1, 1977 ). Article | Zbl 0342.20021 · Zbl 0342.20021 · doi:10.2969/jmsj/02910165 [23] R. STEINBERG , Regular Elements of Semi-Simple Algebraic Groups (I.H.E.S. Pbl. Math., vol. 25, 1965 , p. 49-80). Numdam | MR 31 #4788 | Zbl 0136.30002 · Zbl 0136.30002 · doi:10.1007/BF02684397 [24] R. STEINBERG et T. A. SPRINGER , in A. BOREL et coll., Seminar on Algebraic Groups and Related Finite Groups , Springer LN 131, 1970 . Zbl 0192.36201 · Zbl 0192.36201 · doi:10.1007/BFb0081541 [25] M. SIGIURA , Conjugate Classes of Cartan Subalgebras in Real Semi-Simple Lie algebras (J. Math. Soc. Japon, vol. 11, 1959 , p. 374-434). MR 26 #3827 | Zbl 0204.04201 · Zbl 0204.04201 · doi:10.2969/jmsj/01140374 [26] J. TATE , Number Theoretic Background (Proc. Symp. Pure Math., vol. 33, n^\circ 2, 1979 , p. 3-26). MR 80m:12009 | Zbl 0422.12007 · Zbl 0422.12007 [27] V. S. VARADARAJAN , Harmonic Analysis on Real Reductive Groups , Springer LN 576, 1977 . MR 57 #12789 | Zbl 0354.43001 · Zbl 0354.43001 · doi:10.1007/BFb0097814 [28] N. WALLACH , Representations of Reductive Lie Groups (Proc. Symp. Pure Math., vol. 33, n^\circ 1, 1979 , p. 71-86). MR 80m:22024 | Zbl 0421.22006 · Zbl 0421.22006 [29] N. WALLACH , Harmonic Analysis on Homogeneous Spaces , Marcel Dekker, 1973 . MR 58 #16978 | Zbl 0265.22022 · Zbl 0265.22022 [30] G. WARNER , Harmonic Analysis on Semi-Simple Lie Groups , I-II, Springer, 1972 . · Zbl 0265.22020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.