Discontinuous groups for non-Riemannian homogeneous spaces: Locally symmetric spaces, uniform lattice, deformation of discontinuous groups, rigidity

[P] F. Kassel and T. Kobayashi, Spectral analysis on pseudo-Riemannian locally symmetric spaces, preprint, 6 pages. arXiv: 2001.03292.
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[P] F. Kassel and T. Kobayashi, Spectral analysis on standard locally homogeneous spaces, preprint, 69 pages. arXiv: 1912.12601
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[279] T. Kobayashi, Recent advances in branching laws of representations [hyogen no bunki-soku no saikin no shinten], Sugaku 71 (2019), no. 4, 388-416 (Japanese).
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[278] F. Kassel and T. Kobayashi, Invariant differential operators on spherical homogeneous spaces with overgroups, Journal of Lie Theory 29 (2019), 663-754, arXiv: 1810.02803.
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[258] T. Kobayashi, Global analysis by hidden symmetry, Progr. Math., 323 (2017), pp. 359-397, a special issue in honour of Roger Howe for his 70th birthday. DOI: 10.1007/978-3-319-59728-7_13. arXiv: 160808356.
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[251] T. Kobayashi, Intrinsic sound of anti-de Sitter manifolds, Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics & Statistics, vol. 191, Springer, 2016, pp. 83-99, DOI: 10.1007/978-981-10-2636-2_6. arXiv: 1609.05986.
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[223] F. Kassel and T. Kobayashi, Poincaré series for non-Riemannian locally symmetric spaces, Advances in Mathematics 287, 123-236, DOI: 10.1016/j.aim.2015.08.029. arXiv: 1209.4075.
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[198] T. Kobayashi, From ''localh to ''globalh: Beyond the Riemannian geometry, Kavli IPMU News (2014), no. 25 (March 2014), 4-11.
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[153] F. Kassel and T. Kobayashi, Stable spectrum for pseudo-Riemannian locally symmetric spaces, C. R. Math. Acad. Sci. Paris 349 (2011), no. 1-2, 29-33, DOI: 10.1016/j.crma.2010.11.023.
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[135] T. Kobayashi, Discontinuous groups on pseudo-Riemannian spaces, Mathematische Arbeitstagung 2009, 2009, MPIM2009-40n, 15 pp.
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[126] T. Kobayashi, Hidden symmetries and spectrum of the Laplacian on an indefinite Riemannian manifold, Spectral Analysis in Geometry and Number Theory (in honor of Professor Sunada) (M. Kotani, H. Naito, and T. Tate, eds.), Contemp. Math., vol. 484, Amer. Math. Soc., Providence, RI, 2009, pp. 73-87.
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[124] T. Kobayashi, On discontinuous group actions on non-Riemannian homogeneous spaces, Sugaku Expositions 22 (2009), Amer. Math. Soc., 1-19; a translation by Miles Reid of the original article in Japanese. math.DG/0603319.
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[117] T. Kobayashi, Rigidity and deformation of discontinuous groups for non-Riemannian symmetric spaces (in Japanese), RIMS Kôkyûroku Bessatsu B7 (2008), Representation Theory and Analysis on Homogeneous Spaces (H. Sekiguchi, ed.), pp.1-12.
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[96] T. Kobayashi and S. Nasrin, Deformation of properly discontinuous actions of Zk on Rk+1, Internat. J. Math. 17 (2006), no. 10, 1175-1193, math.DG/0603318.
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[95] T. Kobayashi and S. Nasrin, Deformation space of discontinuous groups Zk for a nilmanifold Rk+1, Surikaiseki Kokyuroku, RIMS 1467 (2006), 101-111, Representation Theory of Groups and Extension of Harmonic Analysis (edited by T. Kawazoe).
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[89] T. Kobayashi and T. Yoshino, Compact Clifford-Klein forms of symmetric spaces - revisited, Pure and Appl. Math. Quarterly 1 (2005), 603-684, Special Issue: In Memory of Armand Borel.
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[88] T. Kobayashi, On discontinuous group actions on non-riemannian homogeneous spaces, Sugaku 57 (2005), 267-281 (in Japanese), An English translation is to appear from Amer. Math. Soc.
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[67] T. Kobayashi, Introduction to actions of discrete groups on pseudo-Riemannian homogeneous manifolds, Acta Appl. Math. 73 (2002), 115-131.
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[66] T. Kobayashi, Discontinuous groups for non-Riemannian homogeneous spaces (translation from English), Sugaku no Saisentan, challenge to the 21th century, vol. 1, Springer-Verlag, Tokyo, 2002, pp. 18-73 (in Japanese).
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[63] T. Kobayashi, Discontinuous groups for non-Riemannian homogeneous spaces, Mathematics Unlimited - 2001 and Beyond (B. Engquist and W. Schmid, eds.), Springer-Verlag, 2001, pp. 723-747.
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[52] T. Kobayashi, Deformation of compact Clifford-Klein forms of indefinite-Riemannian homogeneous manifolds, Math. Ann. 310 (1998), no. 3, 395-409.
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[49] T. Kobayashi and T. Oda, A vanishing theorem for modular symbols on locally symmetric spaces, Comment. Math. Helv. 73 (1998), 45-70.
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[40] T. Kobayashi, Monastir Seminar on proper actions, discontinuous groups, and uniform lattices for pseudo-Riemannian homogeneous manifolds, Proceedings of the CIMPA School, held in Tunisia, July-August 1996 (P. Torasso in Poitiers, ed.), 1997.
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[37] T. Kobayashi, A vanishing theorem of modular symbols on locally symmetric varieties, (notes taken by S. Ishikawa), Proceedings of Representation Theory and Related Topics, Kurashiki 1996 (N. Shimeno, ed.), 1996, pp. 1-16 (in Japanese).
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[36] T. Kobayashi, Discontinuous groups and Clifford-Klein forms of pseudo-Riemannian homogeneous manifolds, Algebraic and Analytic Methods in Representation Theory (H. Schlichtkrull and B. Ørsted, eds.), Perspectives in Mathematics, vol. 17, Academic Press, 1996, pp. 99-165, ISBN 0-12-625440-0.
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[35] T. Kobayashi, Criterion for proper actions on homogeneous spaces of reductive groups, J. Lie Theory 6 (1996), no. 2, 147-163.
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[31] T. Kobayashi, Discontinuous groups acting on homogeneous spaces - Calabi-Markus phenomenon, compact Clifford-Klein forms, Lecture notes of European School on Group Theory held at Sandbjerg Gods', August 15-26, 1994, 30 pp.
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[26] T. Kobayashi, On discontinuous groups acting on homogeneous spaces with noncompact isotropy subgroups, J. Geom. Physics 12 (1993), 133-144.
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[23] T. Kobayashi, A necessary condition for the existence of compact Clifford-Klein forms of homogeneous spaces of reductive type, Duke Math. J. 67 (1992), 653-664.
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[22] T. Kobayashi, Discontinuous groups acting on homogeneous spaces of reductive type, Proceedings of Representation Theory of Lie Groups and Lie Algebras, Fuji-Kawaguchiko, 1990 (T. Kawazoe, T. Oshima, and S. Sano, eds.), World Scientific, 1992, pp. 59-75, ISBN 9810210906.
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[17] T. Kobayashi, Discontinuous group in a homogeneous space of reductive type, Seminar Reports of Unitary Representation 10 (1990), 41-45, at the International Conference on Representation Theories of Lie Groups and Lie Algebras at Lake-Kawaguchi.
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[16] T. Kobayashi and K. Ono, Note on Hirzebruch's proportionality principle, Jour. Fac. Sci. Univ. Tokyo 37 (1990), no. 1, 71-87.
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[15] T. Kobayashi, Discontinuous groups acting on non-Riemannian homogeneous spaces, Surikaiseki Kokyuroku, RIMS 737 (1990), 6-29, Workshop on Algebraic Groups and Related Topics (organized by I. Satake).
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[12] T. Kobayashi, Homogeneous spaces with indefinite-metric and discontinuous groups, 36th Symposium on Differential Geometry, 1989, pp. 104-116 (in Japanese).
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[9] T. Kobayashi, Proper action on a homogeneous space of reductive type, Math. Ann. 285 (1989), no. 2, 249-263.
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[6] T. Kobayashi and K. Ono, Note on Hirzebruch's proportionality principle, Surikaiseki Kokyuroku, RIMS 700 (1989), 103-126, Representation Theory and its Applications to Physics (organized by Y. Kanie).
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[5] T. Kobayashi, Properly discontinuous actions on reductive homogeneous spaces, Seminar Reports of Unitary Representation 8 (1988), 17-22 (in Japanese), at the annual conference on unitary representation theory at Lake-Kawaguchi (organized by H. Yamada), December 1988.
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Updated: 12 Feb 2020

© Toshiyuki Kobayashi