1989 Fiscal Year Annual Research Report

階別り一環の幾何学

Research Project

Project/Area Number	01540074
Research Institution	Sophia University
Principal Investigator	金行壯二上智大学, 理工学部, 教授 (40022553)
Co-Investigator(Kenkyū-buntansha)	田原秀敏上智大学, 理工学部, 助手 (60101028) 野海正俊上智大学, 理工学部, 助手 (80164672) 横沼健雄上智大学, 理工学部, 教授 (00053645) 加藤昌英上智大学, 理工学部, 教授 (90062679) 長野正上智大学, 理工学部, 教授 (10189144)
Keywords	因果構造 / 階別り一環 / 対称空間 / ジ-ゲル領域 / 射影構造 / 特性〓を表わす微分形式 / Gevrey族 / ヴァ-テックス作用素
Research Abstract	1.シロフ境界の因果構造の研究(金行)。柱状対称有界領域D(次元>1)のシロフ境界Sに、或自己共役錐体をモデルとする因果構造を導入した。そしてその自己同型群を決定した。この群の作用はDの内部へのびてDの金正則変換郡を与へしかもそれで一杯であることを示した。2.擬ケ-ラ-アフィン対称空間の研究(金行)。Kε型の擬ケ-ラ-単純既約対称空間(7つある)を階別り一環を用いて統一的に構成しその正則埋込を作った。これによりこの種の対称空間のある稠密開集合は、拡張されたいみのジ-ゲル領域として実現できることを示した。前年度に研究したジョルダン代数に対するシルヴェスタ-の慣性律が証明に使われる。3.クラスL(=射影直線の近傍と正則同値な領域を含む)3次元複素曲面の構造の研究(加藤)。4.複素射影接続をもつ複素多様体にワイルの射影曲率テンソルを用いて新しい特性形式を導入した。そしてチャ-ン特性形式との関係を調べた(加藤)。5.トロイダルリ一環とヴァ-テックス表現の研究(横沼)。C[s,s^<-1>,t,t^<-1>]【cross product】〓(〓は複素単純り一環)の普遍中心拡大の、ヴァ-テックス作用素を用いた表現の構成(横沼)。6.特異点をもつ線型微分方程式に対してかなり一般的条件の下で局所可解性空理を示した(田原)。7.Briot-Bouguet型特異点をもつ非線型偏微分方程式のすべての解の決定(田原)。8.Gevrey級の発散形式解の研究とMaillet型定理の一般化(田原)。9.量子等質空間SU_q(n+1)/SU_q(n)上の帯球函数の研究(野海)。10.2次元量子球面と大gヤコビ多項式についての研究(野海)。

Research Products

(24 results)

All Other

All Publications (24 results)

[Publications] S.Kaneyuki: "On the causal structures of the Silov boundaries of symmetric bounded domains" Lecture Notes in Mathematics,Springer.
[Publications] S.Kaneyuki: "Pseudo-homitian symmetric spaces and Siegel domains over non-degenerate cones" プレプリント.
[Publications] T.Nagano,M.Sumi: "The structure of symmetric spaces with applications" Geometry of Manifolds(論文集)(Academic Press). 111-128 (1989)
[Publications] Ma.Kato: "Factorization of compact complex 3-folds which admit certain projective structures" Tohoku Mathematical Journal. 41. 359-397 (1989)
[Publications] Ma.Kato: "On characteristic forms on complex manifolds" Journal of Algebra.
[Publications] Ma.Kato: "Examples on an extersion Problem of holomorphic mappings and a holomorphic foliation" Tokyo Journal of Mathematics.
[Publications] R.V.Moody S.Eswara Rao T.Yokonuma: "Toroidal Lie algebras and vertex representations" プレプリント.
[Publications] S.Ouchi: "The behavior near the characteristic surface of singular solutions of linear partial differential equations in complex domain" Proceeding Japan Academy. 65. 102-105 (1989)
[Publications] S.Ouchi: "An integral representation of singular solutions and removalle singularities of solutions to linear partial differential equations" プレプリント.
[Publications] H.Tahara: "Singular hyperbolic systems VIII.A symptotic analysis for Fuchsian hyperbolic equations in Gevrey class(2)" Japanese Journal of Mathematics. 15. (1989)
[Publications] H.Tahara: "Solvalility in distributions for a class of singular differential equations III" Publications RIMS,Kyoto University. 26. (1990)
[Publications] R.Gerard H.Tahara: "Nonlinear singular first order partial differential equations of Briot-Bouquet type" プレプリント.
[Publications] R.Gerard H.Tahara: "Holomorphic and singular solutions of mnlinear singular first order partial differential equations" プレプリント.
[Publications] R.Gerard H.Tahara: "Famal solutions in Gevrey classes of nonlinear singular partial differential equations" プレプリント.
[Publications] M.Noumi,H.Yamada,K.Mimachi: "Zonal spherical functions on the quantum homogeneous space SU_q(n+1)/SU_q(n)" Proceeding Japan Academy. 65. 169-171 (1989)
[Publications] T.Masuda,K.Mimachi,Y.Nakagami,M.Noumi,K.Ueno: "Representations of the quantum group SU_q(2)and the little q-Jacobi polynomials" Journal of Functional Analysis.
[Publications] T.Masuda,K.Mimachi,Y.Nakagami,M.Noumi,K.Ueno: "Representations of quantum groups" "Mappings of Operator Algebras"Proceedings of th 1988 Japan-US Joint Seminal.
[Publications] M.Noumi,K.Mimachi: "Quantum 2-spheres and lig q-Jacoli polynomials" Communications of Mathematical Physics.
[Publications] M.Noumi K.Mimachi: "Spherical functions on a family of quantum 3-spheres" プレプリント.
[Publications] K.Shinoda Y.Nakada: "The character of a maximal parabolic sulgunp of GLn(F_q)" Tokyo Journal of Mathematics.
[Publications] A.Rudralis K.Shinoda: "On counting some elements in finite classical groups" プレプリント.
[Publications] H.Sawada: "On a certain covariant representation functor and irrecluable modules of Chevalley groups" Archiv fiir Mathematik. 52. 530-538 (1989)
[Publications] K.Nishizawa K.Yoshino: "Fractal aspects of localization of algebraic integers and complex dynamic systems" Proceeding Japan Academy. 66. (1990)
[Publications] 河田敬義,関口晃司: "標数Pの局所類体論(上智大学数学講究録 No.30)" 上智大学数学教室, 198 (1989)

1989 Fiscal Year Annual Research Report

階別り一環の幾何学

Principal Investigator

金行 壯二 上智大学, 理工学部, 教授 (40022553)

Research Products

[Publications] S.Kaneyuki: "On the causal structures of the Silov boundaries of symmetric bounded domains" Lecture Notes in Mathematics,Springer.

[Publications] S.Kaneyuki: "Pseudo-homitian symmetric spaces and Siegel domains over non-degenerate cones" プレプリント.

[Publications] T.Nagano,M.Sumi: "The structure of symmetric spaces with applications" Geometry of Manifolds(論文集)(Academic Press). 111-128 (1989)

[Publications] Ma.Kato: "Factorization of compact complex 3-folds which admit certain projective structures" Tohoku Mathematical Journal. 41. 359-397 (1989)

[Publications] Ma.Kato: "On characteristic forms on complex manifolds" Journal of Algebra.

[Publications] Ma.Kato: "Examples on an extersion Problem of holomorphic mappings and a holomorphic foliation" Tokyo Journal of Mathematics.

[Publications] R.V.Moody S.Eswara Rao T.Yokonuma: "Toroidal Lie algebras and vertex representations" プレプリント.

[Publications] S.Ouchi: "The behavior near the characteristic surface of singular solutions of linear partial differential equations in complex domain" Proceeding Japan Academy. 65. 102-105 (1989)

[Publications] S.Ouchi: "An integral representation of singular solutions and removalle singularities of solutions to linear partial differential equations" プレプリント.

[Publications] H.Tahara: "Singular hyperbolic systems VIII.A symptotic analysis for Fuchsian hyperbolic equations in Gevrey class(2)" Japanese Journal of Mathematics. 15. (1989)

[Publications] H.Tahara: "Solvalility in distributions for a class of singular differential equations III" Publications RIMS,Kyoto University. 26. (1990)

[Publications] R.Gerard H.Tahara: "Nonlinear singular first order partial differential equations of Briot-Bouquet type" プレプリント.

[Publications] R.Gerard H.Tahara: "Holomorphic and singular solutions of mnlinear singular first order partial differential equations" プレプリント.

[Publications] R.Gerard H.Tahara: "Famal solutions in Gevrey classes of nonlinear singular partial differential equations" プレプリント.

[Publications] M.Noumi,H.Yamada,K.Mimachi: "Zonal spherical functions on the quantum homogeneous space SU_q(n+1)/SU_q(n)" Proceeding Japan Academy. 65. 169-171 (1989)

[Publications] T.Masuda,K.Mimachi,Y.Nakagami,M.Noumi,K.Ueno: "Representations of the quantum group SU_q(2)and the little q-Jacobi polynomials" Journal of Functional Analysis.

[Publications] T.Masuda,K.Mimachi,Y.Nakagami,M.Noumi,K.Ueno: "Representations of quantum groups" "Mappings of Operator Algebras"Proceedings of th 1988 Japan-US Joint Seminal.

[Publications] M.Noumi,K.Mimachi: "Quantum 2-spheres and lig q-Jacoli polynomials" Communications of Mathematical Physics.

[Publications] M.Noumi K.Mimachi: "Spherical functions on a family of quantum 3-spheres" プレプリント.

[Publications] K.Shinoda Y.Nakada: "The character of a maximal parabolic sulgunp of GLn(F_q)" Tokyo Journal of Mathematics.

[Publications] A.Rudralis K.Shinoda: "On counting some elements in finite classical groups" プレプリント.

[Publications] H.Sawada: "On a certain covariant representation functor and irrecluable modules of Chevalley groups" Archiv fiir Mathematik. 52. 530-538 (1989)

[Publications] K.Nishizawa K.Yoshino: "Fractal aspects of localization of algebraic integers and complex dynamic systems" Proceeding Japan Academy. 66. (1990)

[Publications] 河田敬義,関口晃司: "標数Pの局所類体論(上智大学数学講究録 No.30)" 上智大学数学教室, 198 (1989)

金行壯二上智大学, 理工学部, 教授 (40022553)