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講 座 |
大域幾何学大講座 教授 |
研究分野 |
対称性と大域幾何学・大域解析学 |
研究テーマ |
リー群と無限次元表現論,非可換調和解析,不連続群論,積分幾何 |
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研究概要 |
主に次のテーマに関して研究を行っている
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局所的に均質な空間の大域幾何(不連続群論)
- 無限次元の対称性の破れを代数的に記述する理論(表現の分岐則)
- 極小表現における大域解析
- 複素多様体における「可視的作用」の概念と、それを用いた無重複表現の
研究
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主要論文 |
- T. Kobayashi, A program for branching problems in the representation
theory of real reductive groups, Progress in Mathematics, 312,
Birkhauser, 312 (2015), pp. 277-322,
(Vogan教授還暦の Special Volume).
- T. Kobayashi, Visible actions on symmetric spaces, Transformation Groups, 12 (2007), 671-694.
- T. Kobayashi and G. Mano, The inversion formula and holomorphic extension of the minimal representation of the conformal group, in Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory, (R. Howe 教授還暦の Special Volume), 2007, pp. 159-223.
- T. Kobayashi and T. Yoshino, Compact Clifford-Klein forms of symmetric spaces: revisited, Pure and Appl. Math. Quarterly 1 (2005), 603-684, (A. Borel 教授追悼の Special Issue).
- T. Kobayashi, Multiplicity-free representations and visible actions on complex manifolds, Publ. RIMS 41 (2005), 497-549, (RIMS 40周年記念の Special Issue).
- T. Kobayashi and B. Ørsted, Analysis on minimal representations of O(p,q), Part I -- Realization and conformal geometry, Adv. Math. 180 (2003), 486-512; Part II -- Branching laws, Adv. Math. 180 (2003), 513-550; Part III -- Ultra-hyperbolic equations on R p-1,q-1, Adv. Math. 180 (2003), 551-595.
- T. Kobayashi, Branching problems of unitary representations, Proc. of ICM, Beijing 2002, 2 (2002), 615-627.
- T. Kobayashi, Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups III: restriction of Harish-Chandra modules and associated varieties, Invent. Math. 131 (1998), 229-256.
- T. Kobayashi, Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups II: micro-local analysis and asymptotic K-support, Annals of Math. 147 (1998), 709-729.
- T. Kobayashi, Invariant measures on homogeneous manifolds of reductive type, J. reine und angew. Math. 490 (1997), 37-53.
- T. Kobayashi, Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups and its applications, Invent. Math. 117 (1994), 181-205.
- 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.
- T. Kobayashi, Proper action on a homogeneous space of reductive type, Math. Ann. 285 (1989), 249-263.
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著書 |
- T. Kobayashi; B. Speh (2015). Symmetry breaking for
representations of rank one orthogonal groups. アメリカ数学会. ISBN 978-
1-4704-1922-6.
- T. Kobayashi and G. Mano, The Schrödinger model for the minimal
representation of the indefinite orthogonal group O(p, q),
Memoirs of the Amer. Math. Soc., 1000, アメリカ数学会, 171 pp.
- 『リー群と表現論』 (大島利雄氏と共著), 岩波書店, 2005, 610 pp.
- T. Kobayashi, Discontinuous groups for non-Riemannian homogeneous spaces, in Mathematics Unlimited -- 2001 and Beyond (B. Engquist and W. Schmid, eds.), Springer-Verlag, 2000, pp. 723-747. (邦訳) 『数学の最先端 21世紀への挑戦』(分担執筆: グロモフ, コンチェビッチ, ファルティングス他), 2002, pp. 18-73
- T. Kobayashi, Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U(p, q; F)/U(p-m, q; F), Memoirs of the Amer. Math. Soc. 462, アメリカ数学会, 1992, 106 pp.
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学会 |
日本数学会,アメリカ数学会 |
受賞 |
日本数学会建部賞 (1997), 日本数学会春季賞 (1999),
大阪科学賞 (2006), 日本学術振興会賞 (2007), フンボルト賞 (2008)
井上学術賞 (2011), 紫綬褒章(2014), JMSJ論文賞(2015)
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活動 |
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