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On the cohomology of congruence subgroups of symplectic groups

Published online by Cambridge University Press:  22 January 2016

K. F. Lai
K. F. Lai*
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong
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This paper is concerned with the cohomology at “infinity” (in the sense of Harder [4], [5]) of a congruence subgroup of the symplectic group G = Sp(2l, R). G is the subgroup of GL(2l, R) consisting of matrices g satisfying tgJg = J where

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 85 , March 1982 , pp. 155 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Borel, A., Some finiteness properties of adele groups over number fields, IHES Publ. Math., 16 (1963), 101–126.Google Scholar
[ 2 ] Borel, A., Cohomology of arithmetic groups, Proc. Int. Congress Math., Vancouver (1974), 435–442.Google Scholar
[ 3 ] Borel, A. and Serre, J.P., Corners and arithmetic groups, Comment. Math. Helvet., 48 (1973), 436–491.Google Scholar
[ 4 ] Harder, G., On the Cohomology of SL2(e), in Lie groups and their representations, Edited by Gelfand I.M., London, (1975), 139–150.Google Scholar
[ 5 ] Harder, G., On the Cohomology of discrete arithmetically defined groups, Proc. Int. Colloq. On Discrete Subgroups of Lie Groups and Applications to Moduli at Bombay (1973), Oxford University Press (1975), 129–160.Google Scholar
[ 6 ] Harish-Chandra, , Automorphic forms on semi-simple Lie groups, Springer Lecture Notes in Math., 62 (1968).Google Scholar
[ 7 ] Kostant, B., Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math., 74 (1961), 329–387.CrossRefGoogle Scholar
[ 8 ] Langlands, R.P., On the functional equations satisfied by Eisenstein series, Springer Lecture Notes in Math., 544 (1976).Google Scholar
[ 9 ] Matsushima, Y. and Murakami, S., On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds, Ann. of Math., 78 (1963), 365–416.CrossRefGoogle Scholar
[10] Schiffmann, G., Integrales d’entrelacement et fonctions de Whittaker, Bull. Soc. Math. France, 99 (1971), 3–72.CrossRefGoogle Scholar
[11] Schwermer, J., Sur la cohomologie des sous-groupes de congruence de SL3(Z), C. R. Acad. Sc. Paris, 283 (1976), 817–820.Google Scholar
[12] Schwermer, J., Eisensteinreihen und die Kohomologie von Kongruenzuntergrupper von SLn(Z), Bonner Mathematische Schriften, 99 (1977).Google Scholar
[13] van Est, W.T., A generalization of the Cartan-Leray spectral sequence, Indag. Math., 20 (1958), 399–413.CrossRefGoogle Scholar
[14] Well, A., Adeles and algebraic groupes, IAS Princeton, (1961).Google Scholar