Cohomologie de sous-groupes discrets et représentations de groupes semi-simples

Borel, Armand

Colloque analyse et topologie, Astérisque, no. 32-33 (1976), pp. 73-112.

[1] A. Borel, "Density properties of certain subgroups of semi-simple groups," Annals of Math. (2) 72 (1960), 179-188. | DOI | MR | Zbl

[2] A. Borel, "Cohomologie réelle stable de groupes $S$-arithmétiques," C. R. Acad. Sci. Paris 274 (1972), 1700-1702. | MR | Zbl

[3] A. Borel, "Stable real cohomology of arithmetic groups," Annales Sci. E.N.S. (4) 7 (1974), 237-272. | EuDML | Numdam | MR | Zbl

[4] A. Borel, "Cohomology of arithmetic groups," Proc. Int. Cong. Math. Vancouver 1974. | MR | Zbl

[5] A. Borel, "Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup" (to appear). | DOI | MR | Zbl

[6] A. Borel et J. Tits, "Groupes réductifs," Publ. Math. I.H.E.S. 27 (1965), 55-150. | DOI | EuDML | MR

[7] A. Borelet J. Tits, "Homomorphismes 'abstraits' de groupes algébriques simples," Annals of Math. (2) 97 (1973), 499-571. | DOI | MR | Zbl

[8] N. Bourbaki, Espaces vectoriels topologiques, Chap. 1 et 2, Act. Sci. Ind. 1189, Paris 1966, Hermann éd. | MR | Zbl

[9] N. Bourbaki, Groupes et algèbres de Lie, Chap. 2, 3, Act. Sci. Ind. 1349, Paris, Hermann éd. 1972. | MR | Zbl

[10] F. Bruhat et J. Tits, "Groupes algébriques simples sur un corps local : cohomologie galoisienne, décompositions d'Iwasawa et de Cartan," C. R. Acad. Sci. Paris 263 (1966), 867-869. | MR | Zbl

[11] W. Casselman, "On a $p$-adic vanishing theorem of Garland," Bull. A.M.S. 80 (1974), 1001-1004. | DOI | MR | Zbl

[12] W. Casselman, "Introduction to the theory of admissible representations of p-adic reductive groups," (to appear).

[13] W. Casselman and D. Wigner, "Continuous cohomology and a conjecture of Serre's," Inv. Mat. 25 (1974), 199-211. | DOI | EuDML | MR | Zbl

[14] C. Delaroche et A. Kirillov, "Sur les relations entre l'espace dual d'un groupe et la structure de ses sous-groupes fermés (d'après D. A. Kajdan)," Sém. Bourbaki 20e année (1967/68), Exp. 343, Benjamin New York. | Numdam | MR | Zbl

[15] P. Delorme, "Sur la $1$-cohomologie des représentations des groupes de Lie semi-simples," C.R. Acad. Sci. Paris 280 (1975), 1101-1103. | MR | Zbl

[16] J. L. Dupont, "Simplicial de Rham cohomology and characteristic classes of flat bundles," Preprint series 1974/75 no. 29, Matematisk Institut, Aarhus Universitet, 36 p. | MR | Zbl

[17] V. T. Van Est, "On the algebraic cohomology concepts in Lie groups II," Proc. Konink. Nederl. Akad. v. Wet. Series A, 58 (1955), 286-294. | MR | Zbl

[18] H. Garland, "On the cohomology of discrete subgroups of $p$-adic groups," Proc. Int. Congr. Math. Vancouver 1974. | MR | Zbl

[19] H. Hecht and W. Schmid, "A proof of Blattner's conjecture" (to appear). | DOI | MR | Zbl

[20] G. Hochschild and G. D. Mostow, "Cohomology of Lie groups," Ill. Jour. Math. 6 (1962), 367-401. | MR | Zbl

[21] R. Hotta and R. Parthasarathy, "A geometric meaning of the multiplicity of integrable discrete classes in $L^2\left(\Gamma \setminus G\right)$, Osaka J. Math. 10 (1973), 211-234. | MR | Zbl

[22] R. Hotta and R. Parthasarathy, "Multiplicity formulae for discrete series," Inv. Mat. 26 (1974), 133-178. | DOI | EuDML | MR | Zbl

[23] R. Hotta and N. Wallach, "On Matsushima's formula for the Betti numbers of locally symmetric spaces" (to appear). | MR | Zbl

[24] D. A. Kajdan, "On the connection of the dual space of a group with the structure of its closed subgroups," Funct. Anal. and appl. 1 (1967), 63-65. | DOI | MR | Zbl

[25] B. Kostant, "On the existence and irreducibility of certain series of representations," Bull. A. M. S. 75 (1969), 627-642. | DOI | MR | Zbl

[26] R. P. Langlands, "Dimension of spaces of automorphic forms," Proc. Symp. pure math. 9 (1966), 235-252, A. M. S., Providence, R. I. | MR | Zbl

[27] S. Lichtenbaum, "Values of zeta-functions, étale cohomology, and algebraic K-theory II, Springer Lecture Notes 342 (1973), 489-499. | MR | Zbl

[28] S. Maclane, Homology, Grund. math. Wiss. 144, Springer Verlag 1963. | MR | Zbl

[29] G. A. Margoulis, "Discrete groups of motions of manifolds of non-positive curvature," Proc. Int. Congress Math. Vancouver, 1974. | MR | Zbl

[30] Y. Matsushima, "On Betti numbers of compact, locally symmetric Riemannian manifolds," Osaka Math. J. 14 (1962), 1-20. | MR | Zbl

[31] Y. Matsushima, "A formula for the Betti numbers of compact locally symmetric Riemannian manifolds," Jour. Diff. Geom. 1 (1967), 99-109. | DOI | MR | Zbl

[32] Y. Matsushima and S. Murakami, "On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds," Annals of Math. (2) 78 (1963), 365-416. | DOI | MR | Zbl

[33] Y. Matsushima and S. Murakami, "On certain cohomology groups attached to hermitian symmetric spaces," Osaka Jour. Math 2 (1965), 1-35. | MR | Zbl

[34] J. Millson, "On the first Betti number of a compact constant negatively curved manifold" (to appear). | MR | Zbl

[35] W. Schmid, "On a conjecture of Langlands," Annals of Math. (2) 93 (1971), 1-42. | DOI | MR | Zbl

[36] E. B. Vinberg, "Some examples of crystallographic groups on Lobacevskii spaces," Mat. Sbornik 7 (1969), 617-622. | DOI | Zbl

[37] N. Wallach, "On the Selberg trace formula in the case of compact quotient" (to appear). | DOI | MR | Zbl

[38] S. P. Wang, "The dual space of semi-simple Lie groups," Amer J. Math. XCI (1969), 921-937. | DOI | MR | Zbl

[39] S. P. Wang, "On density properties of $S$-subgroups of locally compact groups," Annals of Math. (2) 94 (1971), 325-329. | DOI | MR | Zbl