Les représentations des groupes réductifs $p$-adiques et leurs caractères

Cartier, Pierre

Séminaire Bourbaki : vol. 1975/76, exposés 471-488, Séminaire Bourbaki, no. 18 (1977), Exposé no. 471, 22 p.

[1] I.N. Bernshtein - All reductive p-adic groups are tame, Journ. Funct. Anal. and its appl., 8 (1974), p. 91-93. | Zbl

[2] A. Borel et J. Tits - Groupes réductifs, Publ. Math. I.H.E.S., 27 (1965), p. 55-151. | Zbl | MR | Numdam

[3] F. Bruhat et J. Tits - Groupes réductifs sur un corps local I, Publ. Math. I.H.E.S., 41 (1972), p. 5-251. | Zbl | MR | Numdam

[4] P. Cartier - Vecteurs différentiables dans les représentations unitaires des groupes de Lie, Sém. Bourbaki (nov. 1974), exposé 454, Lecture Notes in Maths, vol. 514, Springer-Verlag, Berlin, 1976. | Zbl | MR | Numdam

[5] W. Casselman - An assortment of results on representations of GL2(k) , in Modular Functions of one variable II, p. 1-54, Lecture Notes in Maths, vol. 349, Springer-Verlag, Berlin, 1973. | Zbl | MR

[6] W. Casselman - The restriction of a représentation of GL2(k) to GL2(σ) , Math. Annalen, 206 (1973), p. 311-318. | Zbl

[7] W. Casselman - The Steinberg character as a true character, in Harmonic Analysis on homogeneous spaces, p. 413-417, American Math. Soc., Providence, 1973. | Zbl | MR

[8] J. Dixmier - Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1969. | Zbl | MR

[9] R. Godement - A theory of spherical functions, Trans. A.M.S., 73 (1952), p. 496-556. | Zbl | MR

[10] Harish-Chandra - Harmonic analysis on reductive p-adic groups, in Harmonic Analysis on homogeneous spaces, p. 167-192, American Math. Soc., Providence, 1973. | Zbl | MR

[11] Harish-Chandra (Notes by G. van DIJK) - Harmonic analysis on reductive p-adic groups, Lecture Notes in Maths, vol. 162, Springer-Verlag, Berlin, 1970. | Zbl | MR

[12] R. Howe - Two Conjectures about reductive p-adic groups, in Harmonic Analysis on homogeneous spaces, p. 377-380, American Math. Soc., Providence, 1973. | Zbl | MR

[13] R. Howe - Some qualitative results on the representation theory of GLn over a p-adic field, notes miméographiées.

[14] H. Jacquet - Représentations des groupes linéaires p-adiques, Theory of group representations and harmonic analysis (C.I.M.E., II Ciclo, Montecatini Terme, 1970), Edizioni Cremonese, Rome, 1971, p. 119-220. | Zbl | MR

[15] H. Jacquet and R. Langlands - Automorphic forms on GL(2) , Lecture Notes in Maths, vol. 114, Springer-Verlag, Berlin, 1970. | Zbl | MR

[16] R. Godement and H. Jacquet - Zeta Functions of simple algebras, Lecture Notes in Maths, vol. 260, Springer-Verlag, Berlin, 1972. | Zbl | MR

[17] Ph. Kutzko - Mackey's theorem for non-unitary representations, à paraître. | Zbl

[18] Ph. Kutzko - On the supercuspidal representations of GL2 , à paraître à l'Amer. Journal Math. | Zbl

[19] F.I. Mautner - Spherical functions over p-adic fields, II, Amer. Journ. Math., 86 (1964), p. 171-200. | Zbl | MR

[20] R.R. Rao - Orbital integrals in reductive groups, Ann. of Maths, 96 (1972), p. 505-510. | Zbl | MR

[21] J. Shalika - A theorem on semi-simple P-adic groups, Ann. of Maths, 95 (1972), p. 226-242. | Zbl | MR

[22] J. Shalika - Representations of the two by two unimodular group over local fields, Seminar on Lie group representations, Institute for Advanced Study, Princeton, 1965 (miméographié).

[23] A.J. Silberger - PGL2 over the p-adics : its Representations, Spherical Functions, and Fourier Analysis, Lecture Notes in Maths, vol. 166, Springer-Verlag, Berlin, 1970. | Zbl | MR

[24] G. Van Dijk - Harmonic analysis on reductive p-adic groups (after HarishChandra), Séminaire Bourbaki, (nov. 1970), exposé 387, Lecture Notes in Mathematics, vol. 244, Springer Verlag, Berlin, 1971. | Zbl | MR | Numdam

[25] V.S. Varadarajan - The theory of characters and the discrete series for semisimple Lie groups, in Harmonic Analysis on homogeneous spaces, p. 45-99, American Math. Soc., Providence, 1973. | Zbl | MR

[1'] I.N. Bernshtein et A.V. Zelevinskii - Représentations du groupe GL(n,F) , où F est un corps local non-archimédien (en russe), Uspkhi Math. Nauk, 31 (1976), p. 5-70. | MR

[2'] A. Borel - Admissible representations of a semi-simple group over a local field with vectors fixed under a Iwahori subgroup, Inv. Math., 35(1976), p. 233- 259. | Zbl | MR

[3'] W. Casselman - Some general results in the theory of admissible representations of p-adic reductive groups, notes miméographiées.

[4'] Harish-Chandra - The Characters of reductive p-adic groups, notes miméographiées, Princeton, 1976.

[5'] Harish-Chandra - The Plancherel formula for reductive p-adic groups, notes miméographies, Princeton, 1976.

[6'] R. Howe - Tamely ramified supercuspidal representations of Gln , notes miméographiées.

[7'] R. Howe - The Fourier transform and germs of characters (Case of Gl n over a p-adic field), Math. Annalen, 208 (1974), p. 305-322. | Zbl | MR

[8'] R. Howe - On the principal series of Gln over p-adic fields, Trans. Amer. Math. Soc., 177 (1973), p. 275-286. | Zbl | MR

[9'] R. Howe - On the asymptotic hehavior of matrix coefficients, notes miméographiées.

[10'] R. Howe and A.J. Silberger - Why any unitary principal series representation of SLn over a p-adic field decomposes simpliy, Bull. Amer. Math. Soc., 81 (1975), p. 599-601. | Zbl | MR

[11'] A.J. Silberger - On complementary series, Discrete series, and the Plancherel measure for a p-adic group, notes miméographiées.