Constructions of automorphic forms and related cohomology classes for arithmetic subgroups of $G_2$

Li, Jian-Shu; Schwermer, Joachim

Compositio Mathematica, Tome 87 (1993) no. 1, pp. 45-78.

[1] Adams, J.: Discrete spectrum of the reductive dual pair (0(p, q), Sp(2m)). Invent. Math. 74 (1983), 449-475. | EuDML | MR | Zbl

[2] Borel, A.: Stable real cohomology of arithmetic groups II. In J. Hano et al. eds. Manifolds and Lie Groups. Progress in Maths. vol. 14, pp. 21-55, Boston 1981. | MR | Zbl

[3] Borel, A.: Automorphic L-functions. In Proc. Symp. Pure Maths., vol. 33, II, pp. 27-61, Providence 1979. | MR | Zbl

[4] Borel, A., Casselman, W.: L 2-cohomology of locally symmetric manifolds of finite volume. Duke Math. J. 50 (1983), 625-647. | MR | Zbl

[5] Borel, A., Garland, H.: Laplacian and the discrete spectrum of an arithmetic group. American J. of Maths. 105 (1983), 309-335. | MR | Zbl

[6] Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups. Ann. Math. Studies 94, Princeton 1980. | MR | Zbl

[7] Deligne, P.: La conjecture de Weil I, Publ. IHES 43 (1973), 273-307. | EuDML | Numdam | MR | Zbl

[8] Gelbart, S.: Weil's Representation and the Spectrum of the Metaplectic Group. Lecture Notes in Maths. Vol. 530. Berlin-Heidelberg-New York 1976. | MR | Zbl

[9] Godement, R., Jacquet, H.: Zeta Functions of Simple Algebras. Lecture Notes in Maths., Vol. 260. Berlin -Heidelberg-New York 1972. | MR | Zbl

[10] Harder, G.: On the cohomology of discrete arithmetically defined groups. In Proc. of the Int. Colloq. on Discrete Subgroups of Lie groups and Appl. to Moduli (Bombay 1973), pp. 129-160, Oxford 1975. | MR | Zbl

[11] Harder, G.: On the cohomology of SL2(O). In Lie groups and their representations, Proc. of the summer school on group representations, pp. 139-150, London 1975. | MR | Zbl

[12] Harder, G.: Eisenstein cohomology of arithmetic groups: The case GL2. Inventiones Math. 89 (1987), 37-118. | MR | Zbl

[13] Howe, R.: θ-series and invariant theory. In Automorphic Forms, Representations and L-functions, Proc. Symp. Pure Maths, Vol. 33, I, pp. 275-285, Providence 1979. | Zbl

[14] Howe, R.: On some results of Strichartz and of Rallis and Schiffmann. J. Functional Analysis 32 (1979), 297-303. | MR | Zbl

[15] Humphreys, J.: Introduction to Lie Algebras and Representation Theory, Berlin-Heidelberg- New York 1972. | MR | Zbl

[16] Jacobson, N.: Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo (2) 7 (1958), 55-80. | MR | Zbl

[17] Jacquet, H., Shalika, J.A.: On Euler products and the classification of automorphic representations I, American J. of Maths. 103 (1981), 499-558. | MR | Zbl

[18] Jacquet, H., Shalika, J.A.: A non-vanishing theorem for zeta functions of GLn. Invent. Math. 38 (1976), 1-16. | MR | Zbl

[19] Kashiwara, M., Vergne, M.: On the Segal-Shale-Weil representation and harmonic polynomials. Invent. Math. 44 (1978), 1-47. | MR | Zbl

[20] Kazhdan, D.: Some applications of the Weil representation. J. D'Analyse Math. 32 (1977), 235-248. | MR | Zbl

[21] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. of Math. 74 (1961), 329-387. | MR | Zbl

[22] Labesse, J.-P., Schwermer, J.: On liftings and cusp cohomology of arithmetic groups. Invent. Math. 83 (1986), 383-401. | MR | Zbl

[23] Langlands, R.P.: On the Functional Equations Satisfied by Eisenstein Series. Lecture Notes in Maths. Vol. 544. Berlin-Heidelberg -New York 1976. | MR | Zbl

[24] Langlands, R.P.: Euler products. New Haven 1971. | MR | Zbl

[25] Li, J.-S.:Singular unitary representations of classical groups. Invent. Math. 97 (1989), 237-255. | MR | Zbl

[26] Li, J.-S.:Theta lifting for unitary representations with non-zero cohomology. Duke Math. J. 61 (1990), 913-937. | MR | Zbl

[27] Li, J.-S.: Non-vanishing theorems for the cohomology of certain arithmetic quotients. J. reine angew. Math. 428 (1992), 177-217. | Zbl

[28] Margulis, G.A.: Arithmeticity of irreducible lattices in semi simple groups of rank greater than 1. Invent. Math. 76 (1984), 93-120. | MR | Zbl

[29] Moeglin, C.: Correspondence de Howe pour les paires reductives duales. Quelques calculs dans le cas archimédien. J. Functional Analysis 85 (1989), 1-85. | MR | Zbl

[30] Moeglin, C., Vigneras, M.F., Waldspurger, J.L.: Correspondances de Howe sur un Corps p-adique. Lecture Notes in Maths. Vol. 1291. Berlin-Heidelberg-New York 1987. | MR | Zbl

[31] Moeglin, C., Waldspurger, J.-L.: Décomposition Spectrale et Series d'Eisenstein-Une paraphrase de l'Ecriture -Paris 1991. | Zbl

[32] Oda, T., Schwermer, J.: Mixed Hodge structures and automorphic forms for Siegel modular varieties of degree two. Math. Ann. 286 (1990), 481-509. | MR | Zbl

[33] Rallis, S.: Injectivity properties of liftings associated to Weil representations. Compositio Math. 52 (1984), 139-169. | Numdam | MR | Zbl

[34] Rallis, S., Schiffmann, G.: Discrete spectrum of the Weil representation. Bull. AMS 83 (1977), 267-270. | MR | Zbl

[35] Rallis, S., Schiffmann, G.: Automorphic cusp forms constructed from the Weil representation. Bull. AMS 83 (1977), 271-275. | MR | Zbl

[36] Rallis, S., Schiffmann, G.: Weil Representation. I. Intertwining Distributions and Discrete Spectrum. Memoirs AMS, Vol. 231, Providence 1980. | MR | Zbl

[37] Rallis, S., Schiffmann, G.: Representations supercuspidales du groupe metaplectique. J. Math. Kyoto Univ. 17 (1977), 567-603. | MR | Zbl

[38] Rallis, S., Schiffmann, G.: Theta correspondence associated to G 2. American J. of Maths. 111 (1989), 801-849. | MR | Zbl

[39] Saito, M.: Representations unitaires des groupes symplectiques. J. Math. Soc. Japan 24 (1972), 232-251. | MR | Zbl

[40] Satake, I.: Spherical functions and Ramanujan conjecture. In Proc. Symp. Pure Maths., Vol. 9, pp. 258-264, Providence 1966. | MR | Zbl

[41] Schafer, R.D.: An Introduction to Non Associative Algebras, New York-London 1966. | Zbl

[42] Schwermer, J.: Kohomologie Arithmetisch Definierter Gruppen und Eisensteinreihen. Lecture Notes in Maths., Vol. 988, Berlin- Heidelberg-New York 1983. | MR | Zbl

[43] Schwermer, J.: On arithmetic quotients of the Siegel upper half space of degree two. Compositio Math. 58 (1986), 233-258. | Numdam | MR | Zbl

[44] Schwermer, J.: Cohomology of arithmetic groups, automorphic forms and L-functions. In Cohomology of Arithmetic Groups and Automorphic Forms. Lecture Notes in Maths., Vol. 1447, pp. 1-29 Berlin- Heidelberg-New York 1990. | MR | Zbl

[45] Schwermer, J.: On residues of Eisenstein series and associated cohomology classes for arithmetic groups. In preparation.

[46] Silberger, A.: Introduction to Harmonic Analysis on Reductive p-adic Groups, Mathematical Notes, Vol. 23, Princeton 1979. | MR | Zbl

[47] Shahidi, F.: On the Ramanujan conjecture and finiteness of poles for certain L-functions. Ann. Maths. 127 (1988), 547-584. | MR | Zbl

[48] Shahidi, F.: Third symmetric power L-functions for GL(2). Compositio Math. 70 (1989), 245-273. | Numdam | MR | Zbl

[49] Shahidi, F.: Langlands' conjecture on Plancherel measures for p-adic groups. In W. Barker and P. Sally eds., Harmonic Analysis on Reductive Groups, Progress in Maths., Vol. 101, pp. 277-295, Boston 1991. | MR | Zbl

[50] Shahidi, F.: On certain L-functions, Amer. J. Math. 103 (1981), 297-356. | MR | Zbl

[51] Vogan, D.A. Jr.: Representations of Real Reductive Lie Groups. Boston-Basel-Stuttgart 1981. | MR | Zbl

[52] Vogan, D.A. Jr., Zuckerman, G.J.: Unitary representations with non-zero cohomology. Compositio Math. 53 (1984), 51-90. | Numdam | MR | Zbl

[53] Weil, A.: Basic Number Theory, New York 1974. | MR | Zbl