Automorphic representations and Lefschetz numbers
Rohlfs, Jürgen ; Speh, Birgit
Annales scientifiques de l'École Normale Supérieure, Tome 22 (1989), p. 473-499 / Harvested from Numdam
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@article{ASENS_1989_4_22_3_473_0,
     author = {Rohlfs, J\"urgen and Speh, Birgit},
     title = {Automorphic representations and Lefschetz numbers},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {22},
     year = {1989},
     pages = {473-499},
     doi = {10.24033/asens.1589},
     mrnumber = {91d:11057},
     zbl = {0689.22005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1989_4_22_3_473_0}
}

Rohlfs, Jürgen; Speh, Birgit. Automorphic representations and Lefschetz numbers. Annales scientifiques de l'École Normale Supérieure, Tome 22 (1989) pp. 473-499. doi : 10.24033/asens.1589. http://gdmltest.u-ga.fr/item/ASENS_1989_4_22_3_473_0/

[B 1] A. Borel, Introduction aux groupes arithmétiques, Paris, Hermann, 1969. | MR 39 #5577 | Zbl 0186.33202

[B 2] A. Borel, Stable Real Cohomology of Arithmetic Groups II, In : J. HANO et al. Eds. Manifolds and Lie groups (Progress in Math. Vol. 14, Boston, Basel, Stuttgart : Birkhöuser, 1981, pp. 21-25). | MR 83h:22023 | Zbl 0483.57026

[B 3] A. Borel, Compact Clifford-Klein Forms of Symmetric Spaces (Topology, Vol. 2, 1963, pp. 111-122). | MR 26 #3823 | Zbl 0116.38603

[B-M] D. Barbasch and H. Moscovici, L2-Index and the Selberg Trace Formula (J. Funct. Anal., Vol. 53, N° 2, 1983, pp. 151-201). | MR 85j:58137 | Zbl 0537.58039

[B-S] A. Borel and J.-P. Serre, Théorèmes de finitude en cohomologie galoisienne (Comment. Math. Helv., Vol. 39, 1964, pp. 111-196). | MR 31 #5870 | Zbl 0143.05901

[B-W] A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups and Representations of Reductive Groups (Annals of Math. Studies, Princeton, University Press, 1960). | Zbl 0443.22010

[Bou] N. Bourbaki, Groupes et algèbres de Lie, Paris, Hermann, 1968.

[C] R. W. Carter, Simple Groups of Lie Type, London, New York, Sydney, Toronto, J. Wiley & Sons 1972. | MR 53 #10946 | Zbl 0248.20015

[Cl 1] L. Clozel, On Limit Multiplicities of Discrete Series Representations in the Space of Automorphic Forms (Invent. math., Vol. 83, 1986, pp. 265-284. | MR 87g:22012 | Zbl 0582.22012

[Cl 2] L. Clozel, On the Cuspidal Cohomology of Arithmetic Subgroups of SL (2n) and the First Betti Number of Arithmetic 3-Manifolds (Duke. Math. J., Vol. 55, 1987, pp. 475-486). | MR 88m:22022 | Zbl 0648.22007

[DG-W] D. De George and N. Wallach, Limit Formulas for Multiplicities in L2 (Γ\G) (Ann. of Math., Vol. 107, 1978, pp. 133-150). | MR 58 #11231 | Zbl 0397.22007

[E] T. J. Enright, Relative Lie Algebra Cohomology and Unitary Representations of Complex Lie Groups (Duke. Math. J., Vol. 46, 1979, pp. 513-525). | MR 81i:22007 | Zbl 0427.22010

[H 1] G. Harder, On the Cohomology of SL2 (D), In : Lie Groups and their Representations (Proc. of the Summer School on Group Repres., London, Hilger, 1975, pp. 139-150). | MR 54 #12977 | Zbl 0395.57028

[H 2] G. Harder, A Gauss-Bonnet Theorem for Discrete Arithmetically Defined Groups (Ann. Scient. Ec. Norm. Sup., (4), 1971, pp. 409-455). | Numdam | MR 46 #8255 | Zbl 0232.20088

[H-Ch] Harish-Chandra, Automorphic Forms on Semisimple Lie Groups (Lecture Notes in Math., Vol. 62, Berlin, Heidelberg, New York, Springer Verlag, 1968). | MR 38 #1216 | Zbl 0186.04702

[He] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces New York, San Francisco, London, Academic Press, 1978. | MR 80k:53081 | Zbl 0451.53038

[J-L] H. Jacquet and R. P. Langlands, Automorphic Forms on Gl (2) (Lecture Notes in Math., Vol. 114, Berlin, Heidelberg, New York, Springer Verlag, 1970). | MR 53 #5481 | Zbl 0236.12010

[K-Z] A. W. Knapp and G. J. Zuckerman, Classification of Irreducible Tempered Representations of Semisimple Groups (Ann. of Math., Vol. 116, 1982, pp. 389-501). | MR 84h:22034a | Zbl 0516.22011

[K] B. Kostant, Lie Algebra Cohomology and the Generalized Borel-Bott Theorem (Ann. of Math., Vol. 74, 1961, pp. 329-387). | MR 26 #265 | Zbl 0134.03501

[L 1] R. P. Langlands, Dimensions of Spaces of Automorphic Forms (Proc. Symp. Pure Math. IX, A.M.S., 1966, pp. 253-257). | MR 35 #3010 | Zbl 0215.11802

[L 2] R. P. Langlands, Basse Change for Gl (2), Annals of math. studies, Princeton, University Press, 1980. | Zbl 0444.22007

[La] J.-P. Labesse, Cusp Cohomology for Arithmetic Groups, Lecture at the Conference Darstellungstheorie reduktiver Lie-Gruppen und automorphe Darstellungen, Mathematisches Forschungsinstitut Oberwolfach, 1987.

[La-S] J.-P. Labesse and J. Schwermer, On Liftings and Cusp Cohomology of Arithmetic Groups (Invent. math., Vol. 83, 1986, pp. 383-401). | MR 87g:11060 | Zbl 0581.10013

[Le-S] R. Lee and J. Schwermer, The Lefschetz Number of an Involution on the Space of Harmonic Cusp Forms of Sl3 (Invent. math., Vol. 73, 1983, pp. 189-239). | MR 84k:22016 | Zbl 0525.10014

[M] H. Minkowski, Gesammelte Abhandlungen I, Leipzig, Berlin, Teubner.

[R 1] J. Rohlfs, The Lefschetz Number of an Involution on the Space of Classes of Positive Definite Quadratic Forms (Comment. Math. Helv., Vol. 56, 1981, pp. 272-296). | MR 83a:10037 | Zbl 0474.10019

[R 2] J. Rohlfs, On the Cohomology of the Bianchi Modular Groups (Math. Z., Vol. 188, 1985, pp. 253-269). | MR 86e:11042 | Zbl 0545.20036

[R 3] J. Rohlfs, Lefschetz Numbers for Arithmetic Groups (in preparation).

[R-S 1] J. Rohlfs and B. Speh, A Cohomological Method for the Determination of Limit Multiplicities (Lecture Notes in Math., Vol. 1243, 1987, pp. 262-272). | MR 88f:22048 | Zbl 0631.22011

[R-S 2] J. Rohlfs and B. Speh, On Limit Multiplicities of Representations with Cohomology in the Cuspidal Spectrum (Duke Math. Journ., Vol. 55, 1987, pp. 199-211). | MR 88k:22010 | Zbl 0626.22008

[R-S 3] J. Rohlfs and B. Speh, Representations with Cohomology in the Discrete Spectrum of Subgroups of SO (n, 1) (ℤ) and Lefschetz Numbers, (Ann. scient. Ec. Norm. Sup., 4e série, T. 20, 1987, pp. 89-136). | Numdam | MR 88h:22019 | Zbl 0626.22010

[Sa] G. Savin, Limit Multiplicities of Cusp Forms (Invent. math., Vol. 95, 1989, pp. 149-159). | MR 90c:22035 | Zbl 0673.22003

[Sch] W. Scharlau, Quadratic and Hermitian Forms, Berlin, Heidelberg, New York, Tokyo, Springer Verlag, 1985. | MR 86k:11022 | Zbl 0584.10010

[Sh] G. Shimura, Sur les intégrales attachées aux formes automorphes (J. Math. Soc. Japan, Vol. 11, No. 4, 1959, pp. 291-311). | MR 22 #11126 | Zbl 0090.05503

[Se] J.-P. Serre, Cohomologie Galoisienne (Lecture notes in Mathematics, No. 5, Berlin, Heidelberg, New York, Springer Verlag). | Zbl 0136.02801

[Sp] B. Speh, Unitary Representations of Gl (n, ℝ) with Non-Trivial (g, ŧ)-Cohomology (Invent. math., Vol. 71, 1983, pp. 1-38). | MR 84k:22024 | Zbl 0505.22015

[V-Z] D. Vogan and G. Zuckerman, Unitary Representations with Nonzero Cohomology (Compositio. Math., Vol. 53, 1984, pp. 51-90). | Numdam | MR 86k:22040 | Zbl 0692.22008

[Z] D. P. Želobenko, The Analysis of Irreducibility in a Class of Elementary Representations of a Complex Semisimple Lie Group (Math. U.S.S.R. Izvestija, 2, 1968, pp. 105-128). | Zbl 0205.04404