Geodesic
Construction of discrete series for classical 𝑝-adic groups
Mœglin, Colette 1   ; Tadić, Marko 2
1 Institut de Mathématiques de Jussieu, CNRS, F-75251 Paris Cedex 05, France
2 Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 715-786 Cet article a éte moissonné depuis la source American Mathematical Society

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The classification of irreducible square integrable representations of classical $p$-adic groups is completed in this paper, under a natural local assumption. Further, this classification gives a parameterization of irreducible tempered representations of these groups. Therefore, it implies a classification of the non-unitary duals of these groups (modulo cuspidal data). The classification of irreducible square integrable representations is directly related to the parameterization of irreducible square integrable representations in terms of dual objects, which is predicted by Langlands program.
DOI : 10.1090/S0894-0347-02-00389-2

Mœglin, Colette  1   ; Tadić, Marko  2

1 Institut de Mathématiques de Jussieu, CNRS, F-75251 Paris Cedex 05, France
2 Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia 
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Mœglin, Colette; Tadić, Marko. Construction of discrete series for classical 𝑝-adic groups. Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 715-786. doi: 10.1090/S0894-0347-02-00389-2

[1] Adams, J. 𝐿-functoriality for dual pairs Astérisque 1989 85 129

[2] Arthur, James Unipotent automorphic representations: global motivation 1990 1 75

[3] Ban, Dubravka Parabolic induction and Jacquet modules of representations of 𝑂(2𝑛,𝐹) Glas. Mat. Ser. III 1999 147 185

[4] Bernstein, I. N., Zelevinsky, A. V. Induced representations of reductive 𝔭-adic groups. I Ann. Sci. École Norm. Sup. (4) 1977 441 472

[5] Goldberg, David Reducibility of induced representations for 𝑆𝑝(2𝑛) and 𝑆𝑂(𝑛) Amer. J. Math. 1994 1101 1151

[6] Jacquet, H., Piatetskii-Shapiro, I. I., Shalika, J. A. Rankin-Selberg convolutions Amer. J. Math. 1983 367 464

[7] Jantzen, Chris On supports of induced representations for symplectic and odd-orthogonal groups Amer. J. Math. 1997 1213 1262

[8] Jantzen, Chris On square-integrable representations of classical 𝑝-adic groups. II Represent. Theory 2000 127 180

[9] Kazhdan, David, Lusztig, George Proof of the Deligne-Langlands conjecture for Hecke algebras Invent. Math. 1987 153 215

[10] Kudla, Stephen S., Rallis, Stephen A regularized Siegel-Weil formula: the first term identity Ann. of Math. (2) 1994 1 80

[11] Mœglin, C. Normalisation des opérateurs d’entrelacement et réductibilité des induites de cuspidales Ann. of Math. (2) 2000 817 847

[12] Mœglin, C. Représentations quadratiques unipotentes des groupes classiques 𝑝-adiques Duke Math. J. 1996 267 332

[13] Mœglin, Colette Non nullité de certains relêvements par séries théta J. Lie Theory 1997 201 229

[14] Mœglin, Colette, Vignéras, Marie-France, Waldspurger, Jean-Loup Correspondances de Howe sur un corps 𝑝-adique 1987

[15] Mœglin, C., Waldspurger, J.-L. Le spectre résiduel de 𝐺𝐿(𝑛) Ann. Sci. École Norm. Sup. (4) 1989 605 674

[16] Muić, Goran On generic irreducible representations of 𝑆𝑝(𝑛,𝐹) and 𝑆𝑂(2𝑛+1,𝐹) Glas. Mat. Ser. III 1998 19 31

[17] Shahidi, Freydoon A proof of Langlands’ conjecture on Plancherel measures Ann. of Math. (2) 1990 273 330

[18] Shahidi, Freydoon On certain 𝐿-functions Amer. J. Math. 1981 297 355

[19] Shahidi, Freydoon Local coefficients and normalization of intertwining operators for 𝐺𝐿(𝑛) Compositio Math. 1983 271 295

[20] Shahidi, Freydoon Twisted endoscopy and reducibility of induced representations for 𝑝-adic groups Duke Math. J. 1992 1 41

[21] Shahidi, Freydoon Fourier transforms of intertwining operators and Plancherel measures for 𝐺𝐿(𝑛) Amer. J. Math. 1984 67 111

[22] Silberger, Allan J. Special representations of reductive 𝑝-adic groups are not integrable Ann. of Math. (2) 1980 571 587

[23] Tadić, Marko On regular square integrable representations of 𝑝-adic groups Amer. J. Math. 1998 159 210

[24] Tadić, Marko On reducibility of parabolic induction Israel J. Math. 1998 29 91

[25] Tadić, Marko Square integrable representations of classical 𝑝-adic groups corresponding to segments Represent. Theory 1999 58 89

[26] Tadić, Marko Structure arising from induction and Jacquet modules of representations of classical 𝑝-adic groups J. Algebra 1995 1 33

[27] Tadić, Marko Representations of 𝑝-adic symplectic groups Compositio Math. 1994 123 181

[28] Vogan, David A., Jr. The local Langlands conjecture 1993 305 379

[29] Waldspurger, J.-L. Un exercice sur 𝐺𝑆𝑝(4,𝐹) et les représentations de Weil Bull. Soc. Math. France 1987 35 69

[30] Zelevinsky, A. V. Induced representations of reductive 𝔭-adic groups. II. On irreducible representations of 𝔊𝔏(𝔫) Ann. Sci. École Norm. Sup. (4) 1980 165 210

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