Toshiyuki KOBAYASHI

Jump To New Home Page (since 2006)

RIMS, Kyoto University,  Sakyo-ku, Kyoto, 606-8502, Japan
Fax: +81-075-753-7276 (secretary)

and

University of Tokyo, Graduate School of Mathematical Sciences, Komaba, Muguro, 153-8914, Japan
toshi@ms.u-tokyo.ac.jp
temporary address:  Harvard University,  Cambridge, MA 02138, USA (Sep.  2000 - Aug. 2001)
                                  MSRI 1000 Centennial Drive, Berkeley, CA 94720 USA (Oct.- Nov., 2001)

Recent Papers and Preprints.

  1. Proper action on a homogeneous space of reductive type, Math.Ann.,285, (1989), 249-263.
  2. 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.
  3. Periodic Schrodinger operators on a manifold, Forum Mathematicum,1 (1989), 69-79, (with K.Ono and T.Sunada).
  4. Note on Hirzebruch's proportionality principle , Jour. Fac. Sci. Univ. Tokyo, (1990), 37, 71-87, (with K.Ono).
  5. 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.
  6. A necessary condition for the existence of compact Clifford-Klein forms of homogeneous spaces of reductive type, Duke Math.J., 67 (1992), 653-664.
  7. 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)
  8. 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. (Abstract,Table of Contents), (see the listings at the A.M.S. Bookstore ; amazon.com).
  9. Perturbations of domains in the Pompeiu problem, Comm. Analysis and Geometry, vol.1 (1993), 29-55.
  10. On discontinuous groups actions on homogeneous spaces with non-compact isotropy subgroups, J. Geometry and Physics, 12 (1993), 133-144.
  11. The Restriction of Aq(l ) to reductive subgroups, Proc. Acad. Japan 69 (1993), 262-267.
  12. 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)
  13. 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.
  14. Harmonic analysis and representation theory on reductive homogeneous spaces, Sugaku, Ronsetsu, vol. 46, Math. Soc. Japan, Iwanami (1994), 124-143, in Japanese.
  15. Discrete decomposability of the restriction of Aq(l ) with respect to reductive subgroups and its applications, Invent. Math., 117 (1994), 181-205.
  16. Criterion of proper actions on homogeneous spaces of reductive groups, J. Lie Theory, vol.6 (1996), 147--163.
  17. The Restriction of Aq(l ) to reductive subgroups II, Proc. Acad. Japan, 71, (1995), 24-26.
  18. 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).
  19. 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.
  20. 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,　vol. 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)
  21. $L^p$-analysis on homogeneous manifolds of reductive type and representation theory, Proc. Japan Acad. vol. 73, (1997), pp. 62--66.
  22. 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.
  23. Invariant measures on homogeneous manifolds of reductive type, J. reine und angew. Math. vol.490, (1997), pp. 37--53.
  24. 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.
  25. A vanishing theorem for modular symbols on locally symmetric spaces, (joint with T.Oda) Comment. Math. Helv. vol.73 (1998), pp. 45--70.
  26. 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.
  27. 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.
  28. Deformation of compact Clifford-Klein forms of indefinite-Riemannian homogeneous manifolds, Math. Ann. vol. 310, (1998), pp. 394--408.
  29. 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.
  30. 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), (translation will appear from A.M.S.).
  31. Discretely decomposable restrictions of  unitary representations of reductive Lie groups  --- examples and conjectures, Advanced Study in Pure Mathematics, 26, (2000), 98--126.
  32. Discontinuous groups for non-Riemannian homogeneous spaces,  in  Mathematics Unlimited -- 2001 and Beyond, (eds. Enguist/Schmid), (2000), 723--748, Springer-Verlag.
  33. Analysis on the minimal representation of $O(p,q)$   --  I..  Realization via conformal geometry , (joint with B.Orsted).
  34. Analysis on the minimal representation of $O(p,q)$   --  II .Branching laws , (joint with B.Orsted).
  35. Analysis on the minimal representation of $O(p,q)$   --  III..  Ultrahyperbolic equations on R^{p-1,q-1} , (joint with B.Orsted).

 Books

  1.    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.
  2.    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.
      A  list of errata (as of April, 2001) is available in  Dviform.

      A second printing (ISBN4-00-011007-1 C334) was published in June 2001.
 

Others (not complete)

  1. Properly discontinuous actions on homogeneous spaces of reductive type, Seminar Reports of Unitary Representation Theory, vol. 8, (1988), 17-22, in Japanese.
  2. Discontinuous groups and homogeneous spaces with indefinite metric, Proc. of the 36-th. Symposium of Geometry, (1989), 104-116, in Japanese.
  3. Unitary representations realized in $L^2$-sections of vector bundles over semisimple symmetric spaces, `Proceedings at the 27-th. Symposium of Functional Analysis and the 28-th Real Analysis at Hirosaki University, July 1989', Mathematical Society of Japan (1989), 39-54, in Japanese.
  4. Discontinuous group in a homogeneous space of reductive type, Seminar Reports of Unitary Representation Theory, vol. 10, (1990), 41-45, (abstract of the ICM-satellite conference at Fuji-Kawaguchiko), in English.
  5. Discontinuous groups acting on non-Riemannian homogeneous spaces, Kokyuroku, RIMS Kyoto University, 737 (1990), 6-29, in English.
  6. How can we VIEW from silhouettes ?, Gendai Sugaku no Ayumi, Vol.4, 1992, 6 pages, (Introduction to non-commutative harmonic analysis, with T.Oshima), Nihon-Hyoronsha, in Japanese.
  7. Introduction to harmonic analysis on spherical homogeneous spaces, `held at Rikkyo University January 1995 and at Yamagata-mura in Nagano August 1995', Proceedings of the 3rd summer school on number theory, Homegeneous Spaces and Automorphc Forms (eds. F.Sato), (1995), pp.22--41, in Japanese.
  8. Vanishing theorem for modular symbols on locally symmetric spaces, (Lecture notes in Japanese, taken by S.Ishikawa), (1996), pp.1-16,Proceedings of "Representation theory and related topics", held at Kurashiki, November 1996, (eds. N.Shimeno).
  9. On the restriction of unitary representations and their applications, Proceedings of the Syposium of Representation Theory held at Mikawa-Heights (eds. Takenaka), November 19--22, 1996, (1996), pp.131--141.
  10. Monastir Seminar on the restriction of unitary representations and their applications, Proceedings of the CIMPA School, held in Tunisia, July-August 1996 (eds. P. Torasso in Poitiers, France), (1997).
  11. 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 (eds. P. Torasso in Poitiers, France), (1997).
  12. Restriction of unitary representations of reductive Lie groups, Abstract of Hayashibara Forum, Representation Theory and Homogeneous Spaces, July 27 -- August 1, 1997. 2 pages.
  13. Discrete branching laws of unitary representations, Abstract at a talk of MSJ meeting (2 pages, in Japanese), 1997.
  14. Invariant measures on homogeneous manifolds of reductive type, Abstract at a talk of MSJ meeting (2 pages, in Japanese), 1997.
  15. Discrete series representations for homogeneous manifolds of reductive type, Abstract at a talk of MSJ meeting (2 pages, in Japanese), 1997.
  16. Conformal geometry, minimal representations, and dual pair correspondence, Abstract at a talk of MSJ meeting (2 pages, in Japanese), 1997.
  17. Invariant measures for homogeneous spaces of reductive type, 2 pages, Abstract of a talk at a conference on "Lie groups and geometry", organizeed by S.Kaneyuki and H.Shima, December 1997 at Yamaguchi University.
  18. Discrete and Continuous --- Branching laws of infinite dimensional representations and their applications, Proceedings of plenary talks at the annual meeting of Mathematical Society of Japan, (Meijo University, Nagoya, March 26--29, 1998), (1998), pp. 35--54.
  19. Compact Clifford-Klein forms of pseudo-Riemannian homogeneous manifolds, Abstract of an international conference "Arthur L. BESSE Round Table in Global Pseudo-Riemannian Geometry" held at Universite Henri Poincare, Nancy (France), June, 1998.
  20. Conformal geometry and minimal unipotent representations, Proceedings of the Symposium on Lie groups and geometry, held at Yokohama urban college, (eds. Asano and S.Kaneyuki), 1998, pp.14--18.
  21. Theory of discrete decomposable branching laws of unitary representations of semisimple Lie groups and its applications, (in Japanese) Lecture for the Spring Prize of Mathematical Society of Japan, March 26, 1999. Proceedings of plenary talks at the annual meeting of Mathematical Society of Japan, (Gakushuin University, March 25--28, 1999), (1999), pp. 1--19.
  22. Discontinuous groups for homogeneous spaces, Symposium on Representation Theory (eds. H.Matumoto), at Tateyama, (1999), 99-110 (in Japanese).
  23. Adjoint Action, Encyclopaedia of Mathematics, (1999) 15--16, Kluwer Academic Publishers.
  24. Book Review of classics (Meicho Fukkatsu), Pontryagin, Continuous Groups, Sugaku-no Tanoshimi, 23, (2000) pp.110-119 (in Japanese).
Toshiyuki KOBAYASHI
RIMS, Kyoto University,  Sakyo-ku, Kyoto, 606-8502, Japan
toshi@kurims.kyoto-u.ac.jp
Fax: +81-075-753-7276 (secretary)