KOBAYASHI, TOSHIYUKI / الرياضيات / الباحثون

المركز الدولي للبحث العلمي

الباحثون

الرياضيات / KOBAYASHI, TOSHIYUKI

Toshims.u-tokyo.ac.jp

الموضع

Professor
RIMS, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan
and University of Tokyo, Graduate School of Mathematical Sciences, Komaba, Muguro, 153-8914, Japan

مواضيع البحث

Lie groups and representation theory

الجوائز

1999 Spring Award of Mathematical Society Japan

المنشورات

Recent Papers and Preprints.

Proper action on a homogeneous space of reductive type, Math.Ann.,285, (1989), 249-263.

Asymptotic behaviours of the null variety for a convex domain in a non-positively curved space form, Jour. Fac. Sci. Univ. Tokyo, 36 (1989), 389-478.

Periodic Schrodinger operators on a manifold, Forum Mathematicum,1 (1989), 69-79, (with K.Ono and T.Sunada).

Note on Hirzebruch's proportionality principle , Jour. Fac. Sci. Univ. Tokyo, (1990), 37, 71-87, (with K.Ono).

Singular unitary representations and discrete Series for indefinite Stiefel manifolds, `Harmonic Analysis on Lie Groups held at Sandbjerg Gods', August 26-30, 1991, edited by N. V. Pedersen, 1991, Mathematical Institute, Copenhagen University, 30-33.

A necessary condition for the existence of compact Clifford-Klein forms of homogeneous spaces of reductive type, Duke Math.J., 67 (1992), 653-664.

Discontinuous groups acting on homogeneous spaces of reductive type, `Proceedings of ICM-90 satellite conference on Representation Theory of Lie Groups and Lie Algebras at Fuji-Kawaguchiko, August 31-September 3, 1990, edited by T.Kawazoe, T.Oshima and S.Sano, World Scientific, Singapore, (ISBN: 9810210906) , (1992), 59-75. (Reference: amazon.com)

Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U(p,q;F)/U(p-m,q;F), Memoirs of the American Math. Soc. Vol.462 (1992), 106 pp. ISBN 0-8128-2524-0.

Perturbations of domains in the Pompeiu problem, Comm. Analysis and Geometry, vol.1 (1993), 29-55.
On discontinuous groups actions on homogeneous spaces with non-compact isotropy subgroups, J. Geometry and Physics, 12 (1993), 133-144.

The Restriction of Aq(l ) to reductive subgroups, Proc. Acad. Japan 69 (1993), 262-267.
Bounded domains and the zero sets of Fourier transforms,`75 Years of Radon Transforms held at Wien, September 1992' edited by S. Gindikin and P. Michor, Conference, Proceedings and Lecture Notes in Mathematical Physics IV, International Press, Hongkong, (1994), 223-239. (Reference: ISBN: 1-57146-008-X , International Press , amazon com)

Discontinuous groups acting on homogeneous spaces ---- Calabi-Markus phenomenon, compact Clifford-Klein forms, `Lecture notes in European School on Group Theory' held at Sandbjerg Gods', August 15-26, 1994, 30 pp., edited by B.Oersted and H.Schlichtkrull.

Harmonic analysis and representation theory on reductive homogeneous spaces, Sugaku, Ronsetsu, vol. 46, Math. Soc. Japan, Iwanami (1994), 124-143, in Japanese.

Discrete decomposability of the restriction of Aq(l ) with respect to reductive subgroups and its applications, Invent. Math., 117 (1994), 181-205.

Criterion of proper actions on homogeneous spaces of reductive groups, J. Lie Theory, vol.6 (1996), 147--163.

The Restriction of Aq(l ) to reductive subgroups II, Proc. Acad. Japan, 71, (1995), 24-26.

Convex domains and the Fourier transform on spaces of constant curvature, (Abstract, Table of Contents), `Lecture notes at CIMPA Spring School held at WuHan University in China', edited by P.Torasso (Poitiers, France) April-May, 1991, 112 pp., to appear in Travaux en Cours, Hermann (Paris).

Harmonic analysis on homogeneous manifolds of reductive type and unitary representation theory, Translations, Series II, vol.183, (1998), 1--31, Selected Papers on Harmonic Analysis, Groups, and Invariants (eds. K. Nomizu), Amer. Math. Soc., ISBN 0-8218-0840-0.

Discontinuous groups and Clifford-Klein forms of pseudo-Riemannian homogeneous manifolds, (Abstract, Table of Contents), Algebraic an d Analytic Methods in Representation Theory, (eds. Schlichtkrull and B. Orsted) Perspectives in Mathematics,$B!!(Bvol. 17, (1996), 99--165, Academic Press, (Lecture Notes of the European School on Group Theory held at Sandbjerg Gods' in August 1994; H.H.Anderson, A.Joseph, T.Kobayashi, V.S.Varadarajan, D.A.Vogan), ISBN 0-12-625440-0. (References: Academic Press Book Catalog; amazon.com)

$L^p$-analysis on homogeneous manifolds of reductive type and representation theory, Proc. Japan Acad. vol. 73, (1997), pp. 62--66.

Multiplicity free branching laws for unitary highest weight modules, Proceedings of Representation Theory held at Saga, Kyushu 1997 (eds. K. Mimachi), (1997), pp. 9--17.

Invariant measures on homogeneous manifolds of reductive type, J. reine und angew. Math. vol.490, (1997), pp. 37--53.

Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups, J. Funct. Anal. vol. 152, (1998) pp. 100--135.

A vanishing theorem for modular symbols on locally symmetric spaces, (joint with T.Oda) Comment. Math. Helv. vol.73 (1998), pp. 45--70.

Conformal geometry and branching laws for unitary representations attached to minimal nilpotent orbits, (joint with B. Orsted), C. R. Acad. Sci. Paris, vol. 326, (1998), pp. 925--930.

Discrete decomposability of the restriction of Aq(l ) with respect to reductive subgroups II ------ micro-local analysis and asymptotic $K$-support, Annals of Math. vol.147, (1998) 709--729.

Deformation of compact Clifford-Klein forms of indefinite-Riemannian homogeneous manifolds, Math. Ann. vol. 310, (1998), pp. 394--408.

Discrete decomposability of the restriction of Aq(l ) with respect to reductive subgroups III --- restriction of Harish-Chandra modules and associated varieties, Abstract, Inventiones Mathematicae, vol. 131, (1998), pp. 229--256.

Theory of discrete decomposable restrictions of unitary representations of semisimple Lie groups and some applications, Sugaku vol. 51, (1999), pp.337--356, Mathematical Society of Japan, (in Japanese).

Discretely decomposable restrictions of unitary representations of reductive Lie groups --- examples and conjectures, Advanced Study in Pure Mathematics, 26, (2000), 98--126.

Discontinuous groups for non-Riemannian homogeneous spaces, in Mathematics Unlimited -- 2001 and Beyond, (eds. Enguist/Schmid), (2000), 723--748, Springer-Verlag.

Analysis on the minimal representation of $O(p,q)$ -- I.. Realization via conformal geometry , (joint with B.Orsted).

Analysis on the minimal representation of $O(p,q)$ -- II .Branching laws , (joint with B.Orsted).

Analysis on the minimal representation of $O(p,q)$ -- III.. Ultrahyperbolic equations on R^{p-1,q-1} , (joint with B.Orsted).


Books

Lie Groups and Lie Algebras I , xvi+293pp, by T.Kobayashi and T.Oshima was published in 1999, by Iwanami in the Iwanami-Kouza series. ISBN4-00-010647-3 C3341, in Japanese.

Lie Groups and Lie Algebras II , xix+314pp, by T.Kobayashi was published in 1999, by Iwanami Shoten in the same series, ISBN4-00-010647-3 C3341, in Japanese.

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