Kashiwara, Masaki(Institute for Advanced Study) | Activity Database on Education and Research, Kyoto University

Kashiwara, Masaki

Institute for Advanced Study Program-Specific Professor

Last Updated :2025/05/27

Basic Information

Professional Memberships

日本数学会

Mathematical Society of Japan

Academic Degree

理学修士(東京大学)

理学博士(京都大学)

Research History

From 1978, To 2002
数理解析研究所助教授，口授

From 1978, To 2002
(Associate)Prof. RIMS, Kyoto U.

From 1973, To 1977
Nagoya University, School of Science

From 1973, To 1977
Associate Prf. Nagoya Univ.

From 1971, To 1973
数理解析研究所助手

From 1971, To 1973
Research Associate, RIMS, Kyoto U.

Language of Instruction

Japanese

ID,URL

J-Global ID
200901051561692779

researchmap URL

https://researchmap.jp/read0092747

Last Updated :2025/05/27

Research

Research Interests

代数解析

Algebraic Analysis

Research Areas

Natural sciences, Basic analysis

Misc.

On Crystal bases of the q-analogue of universal enveloping algebrces
Duke Math. J., 1991

On Crystal bases of the q-analogue of universal enveloping algebrces
Duke Math. J., 1991

Kazhdan-Lusztig conjecture and holonomic systems
Inventiones Math., 1981

Kazhdan-Lusztig conjecture and holonomic systems
Inventiones Math., 1981

B-functions and holonomic systems
Inventiones Math., 1976

B-functions and holonomic systems
Inventiones Math., 1976

On the maximally overdetermined systems of linear differential equations
Publications of RIMS, 1975

On the maximally overdetermined systems of linear differential equations
Publication of RIMS, 1975

Books and Other Publications

代数解析概論
岩波書店, 2000, Not refereed

Sheaves on manifolds
Springer Verlag, 1990, Not refereed

Sheaves on manifolds
Springer Verlag, 1990, Not refereed

Awards

01 Mar. 2025
アーベル賞

02 Aug. 2023
Frontier of Science Award

External funds: Kakenhi

Representation Theory and Algebraic Analysis
Grant-in-Aid for Scientific Research (B)
Basic Section 11010:Algebra-related
Kyoto University
柏原正樹
From 01 Apr. 2020, To 31 Mar. 2025, Granted
代数解析;リーマン・ヒルベルト対応;モノイダル圏化;アフィン量子群;箙ヘッケ環;表現論;量子群;不確定特異点ホロノミック系;クラスター代数;圏化;アフィンヘッケ箙圏
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20H01795/

Global Study of Primitive Forms
Grant-in-Aid for Scientific Research (B)
Basic Section 11020:Geometry-related
Kyoto University;The University of Tokyo
Kyoji Saito
From 01 Apr. 2018, To 31 Mar. 2023, Project Closed
primitive form;elliptic root system;elliptic Lie algebra;elliptic Artin group;elliptic Artin monoid;hyperbolic root system;integrablerepresentation;cuspidal root system;non-cancellative monoid;second homotopy classees;hyperbolic root systems;primitive forms;vertex operator algebra;原始形式;周期領域;楕円リー環;楕円アルティン群;楕円アルティンモノイド;楕円ルート系;モジュラー群作用;楕円周期領域;原始型式;可積分構造;$K(\pi,1)$-conjecture;周期写像;無限次元リー館;可積分系;ホモトピー群;非キャンセラティブ;高次ホモトピー類;ハイパボリック　ルート系;無限次元リー環;表現論;楕円積分;Eisennstein 級数;integrable hierarchy;楕円アルティングン;Drinfeld-Sokorov;安定性条件
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18H01116/

algebraic analysis and representation theory
Grant-in-Aid for Scientific Research (B)
Kyoto University
Masaki Kashiwara
From 01 Apr. 2015, To 31 Mar. 2020, Project Closed
箙ヘッケ環;団代数;モノイダル圏化;アフィン量子群;D加群;副解析層;副構成層;代数解析;リーマン・ヒルベルト対応;表現の圏化;表現論;量子群;不確定特異点ホロノミック系;クラスター代数;圏化
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15H03608/

Geometric triangulated category and associated primitive forms
Grant-in-Aid for Scientific Research (A)
The University of Tokyo
Kyoji Saito
From 01 Apr. 2013, To 31 Mar. 2018, Project Closed
原始形式;鏡像対称性;モノイドの増大関数;逆転公式;ド-ラム複体の直像;楕円リー環;楕円アルティン群;周期写像;skew-growth function;数理;ドラム複体;最高次可積分表現;双対アルティンモノイド;歪増大関数;原始型式;平坦構造;楕円リー群;歪増大函数;モノイド;導来圏;Artin 群;共型場;Geppner特異点;高次種数;安定性条件空間;primitive form;mirror symmetry;pre-potential;good-section;poly-vector field;oscillatory integrals
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25247004/

Algebraic analysis of infinite symmetry
Grant-in-Aid for Scientific Research (B)
Kyoto University
Masaki KASHIWARA
From 01 Apr. 2010, To 31 Mar. 2015, Project Closed
表現論;リーマン・ヒルベルト対応;圏化;量子群;箙ヘッケ環;不確定特異点ホロノミック系;国際研究者交流;イタリア：フランス：アメリカ：韓国;ワイル・シューア双対性;変形量子化;結晶基底;超局所解析
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22340005/

D-modules on infinite-dimensional algebraic varieties and their application to representation theory
Grant-in-Aid for Challenging Exploratory Research
Osaka City University
Toshiyuki TANISAKI
From 01 Apr. 2009, To 31 Mar. 2012, Project Closed
代数解析;群論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21654005/

Derive categories and infinite dimensional Lie allgebras associated with primitive forms
Grant-in-Aid for Scientific Research (B)
The University of Tokyo
Kyoji SAITO
From 08 Apr. 2008, To 31 Mar. 2013, Project Closed
原始形式;三角圏;無限次元リー環;周期写像;行列分解;熱力学的極限関数;モノイドの増大関数;逆転公式;A-型とD-型超越関数;monoid の増大関数;歪増大関数と逆転公式;整係数正方行列環;最小公倍元;Euler積;楕円リー環;無限次元リー環と表現;増大函数;原始形式の周期写像;消滅サイクル;基本群;モノイド;自由エネルギー;増大関数;導来圏;Artin monoid;free divisor;derived Category;matrix factorisation
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340011/

Research on representation theory of algebraic groups and quantum groups via algebraic analysis
Grant-in-Aid for Scientific Research (B)
Osaka City University
Toshiyuki TANISAKI
From 01 Apr. 2007, To 31 Mar. 2010, Project Closed
群の表現論;代数解析;代数群;量子群
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340010/

Algebraic Analysis of Infinite Symmetry
Grant-in-Aid for Scientific Research (B)
Kyoto University
Masaki KASHIWARA
From 01 Apr. 2006, To 31 Mar. 2010, Project Closed
表現論;量子群;結晶基底;変形量子化;アフィンヘッケ環;偏屈層;旗多様体;D-加群
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18340007/

Lie algebras and quantum groups via algebraic analysis
Grant-in-Aid for Scientific Research (B)
Osaka City University
Toshiyuki TANISAKI
From 01 Apr. 2005, To 31 Mar. 2007, Project Closed
リー代数;量子群;代数解析, Lie algebras;Quantum groups;Algebraic analysis
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17340012/

Representation theory of algebraic groups via algebraic analysis
Grant-in-Aid for Scientific Research (C)
Osaka City University
Toshiyuki TANISAKI
From 01 Apr. 2003, To 31 Mar. 2005, Project Closed
代数群;表現;代数解析, algebraic groups;representations;algebraic analysis
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15540041/

Parabolic Kostka polynomials, quiver varieties, crystal bases and tropicalcombinatorics
Grant-in-Aid for Scientific Research (B)
Kyoto University
Anatol N. KIRILLOV
From 01 Apr. 2003, To 31 Mar. 2006, Project Closed
放物型コストカ多項式;トロピカルRSK;Amoebas;トーラス結び目;Virasoro代数;Nichols-Woronowicz代数;Schubert Calculus;平坦接続;Parabolic Kostka polynomials;Tropical RSK;Discrete integrable systems;Nichols algebras;Weyl modules;Flat connections;Generalized saturation theorem;Coxeter groups;Quantum cohomology;Bracket algebra;Schubert polynomials;Sato gra smannian;Associated Askey-Wilson functions, Parabolic Kostka polynomials;Tropical RSK;Amoebas;Torus knots;Virasoro algebra;Nichols-Woronowicz algebras;Schubert Calculus;Flat connections
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340006/

The flag variety of elliptic Lie algebra and elliptic primitive automorphic forms
Grant-in-Aid for Scientific Research (B)
Kyoto University
Kyoji SAITO
From 01 Apr. 2001, To 31 Mar. 2004, Project Closed
楕円ルート系;ブレイド群;原子形式;平坦構造;semi-algebraic geometry;鏡映群;楕円リー環;highest weight表現;エータ関数;原始形式;楕円Lie環;拡大ハイパボリックルート系;最高ウエイト表現;ブロック代数;周期積分;フロベニウス多様体;無限次元リー環;周期写像;拡大アフィン・ルート系;Bruhat分解;Peter-Weyl定理, elliptic root system;braid group;primitive form;flat structure;semi-algebraic geometry;reflection group;elliptic Lie algebra
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13440021/

Representation theory of Lie algebras and quantum groups
Grant-in-Aid for Scientific Research (B)
Osaka City University;Hiroshima University
Toshiyuki TANISAKI
From 01 Apr. 2001, To 31 Mar. 2003, Project Closed
無限次元リー代数;量子群;代数群;最高ウエイトDb群;最高ウェイト加群;カッツ・ムーディ・リー代数, Infimte dimensiand Lie Igobras;quantum groups;algobrarc groups;Highestweight modulas
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13440010/

Algebraic Analysis of Representation Theory
Grant-in-Aid for Scientific Research (B)
KYOTO UNIVERSITY
Masaki KASHIWARA
From 01 Apr. 2001, To 31 Mar. 2005, Project Closed
表現論;結晶基底;量子群;D-加群;幾何学的表現論;可解模型;組み合わせ, representation theory;crystal bases;quantum group;D-modules
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13440006/

Physical Combinatorics
Grant-in-Aid for Scientific Research (A)
Kyoto University
Tetsuji MIWA
From 01 Apr. 2001, To 31 Mar. 2005, Project Closed
頂点作用素代数;ジャック多項式;共形場理論;コストカ多項式;融合積;余不変式;マクドナルド多項式;相関函数;Virasoro代数;XXZ模型;アフィンリー代数;Thirring模型;2重アフィンヘッケ環;フェルミ型公式;アフィンリー環;ヴィラソロ代数;形状因子;ホールリトルウッド多項式;サインゴルドン模型;Jack多項式;Kostka多項式, Vertex operator algebra;Jack Polynomial;conformal field theory;Kostka polynomial;fusion product;coinvariants;Macdonald polynomial;correlation function
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13304010/

Representation theory of algebraic groups through algebraic analysis
Grant-in-Aid for Scientific Research (B).
Hiroshima University
Toshiyuki TANISAKI
From 01 Apr. 1999, To 31 Mar. 2001, Project Closed
代数群;表現論;代数解析;カッツムーディ・リー代数;最高ウェイト加群;量子群, algebraic group;representation;algebraic analysis
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11440009/

有限体およびP進体上のKZ方程式とその表現論への応用
Grant-in-Aid for Exploratory Research
Hiroshima University
谷崎俊之
From 01 Apr. 1998, To 31 Mar. 2000, Project Closed
KZ方程式;表現論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10874005/

Combinatorics in representation theory of classical groups and quantum groups, and applications
Grant-in-Aid for Scientific Research (B).
Nagoya University
Soichi OKADA
From 01 Apr. 1998, To 31 Mar. 2001, Project Closed
古典群の表現;量子群の表現;Young図形;Schur関数;alternating sign matrix;Robinson-Schensted対応;SchurのQ-関数;Kazdan-Lusztig予想;D加群;小行列式の和公式;crystal base, representations;classical groups;quantum groups;Young diagrams;Schur functions;RS correspondence;alternating sign matrix;KL conjecture
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440004/

Primitive Forms and Period Maps
Grant-in-Aid for Scientific Research (B)
KYOTO UNIVERSITY
Kyoji SAITO
From 01 Apr. 1997, To 31 Mar. 2000, Project Closed
原始形式;weight系;楕円ルート系;楕円特異点;楕円ワイル群;楕円リー環;楕円L-函数;平坦構造;平坦座標;楕円アルティン群;原始保型形式;エータ積;Weight系, primitive forms;period maps;elliptic singularities;elliptic root systems;elliptic Lie algebra;elliptic L-functions;regular systems of weights;flat structure
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440031/

Represontation theory of algebraic groups
Grant-in-Aid for Scientific Research (B)
HIROSHIMA UNIVERSITY
Toshiyuki TANISAKI
From 01 Apr. 1997, To 31 Mar. 1999, Project Closed
代数群;リー代数;量子群, algebraic groups;Lie algebras;Quantum groups
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440018/

Algebraic analysis of representation theory
Grant-in-Aid for Scientific Research (A).
KYOTO UNIVERSITY, RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES
Masaki KASHIWARA
From 01 Apr. 1997, To 31 Mar. 2001, Project Closed
表現論;量子群;可解模型;組み合わせ論;組み合せ論;アフィンリー環;代数解析;量子郡;特殊凾数;対称空間, representation theory;quantum groups;solvable models;combinatorics
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304003/

Mathematical analysis and numerical computation of nonlinear partial differential equations
Grant-in-Aid for Scientific Research (B)
KYOTO UNIVERSITY
Hisashi OKAMOTO
From 01 Apr. 1996, To 31 Mar. 1997, Project Closed
流体方程式;特異摂動;代数解析;マトロイド理論;渦層;数値解析法, Equations of motion of fluids;singular perturbation;algebraic analysis;matroid theory;vortex sheet;numerical method
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08454028/

Algebraic analysis of infinite symmetry
Grant-in-Aid for Scientific Research (B)
KYOTO UNIVERSITY
Masaki KASHIWARA
From 01 Apr. 1996, To 31 Mar. 1997, Project Closed
代数解析;無限対称性;可解模型;量子群;結晶基底;相関函数, algebraic analysis;infinite symmetry;solvable model;quantum group;crystal base;correlation function
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08454006/

代数多様体の分類とその上の曲線(共形場理論)
Grant-in-Aid for General Scientific Research (B)
Kyoto University
森重文
From 01 Apr. 1995, To 31 Mar. 1996, Project Closed
curve;algebraic space;Teichmuler space;Euler number;elliptic fibration;terminal singularity;correlation function;XXZ model
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07454016/

非可換解析学の研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
荒木不二洋
From 01 Apr. 1994, To 31 Mar. 1995, Project Closed
指標公式;WKB解析;組み紐群;b関数;2次元量子重力場;同変ホモトピー型;非可換解析
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640232/

代数多様体上の大城解析
Grant-in-Aid for General Scientific Research (B)
Kyoto University
宮岡洋一
From 01 Apr. 1994, To 31 Mar. 1995, Project Closed
有理曲線;Fano多様化;単有理性;極小モデル;コンパクト化;商特異点;実代数多様体;Galois群
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06452007/

Synthetic Study of Fundamantal Mathematics
Grant-in-Aid for Scientific Research (A)
Nagoya University
Shigeru MUKAI
From 01 Apr. 1994, To 31 Mar. 1997, Project Closed
代数的組せ論;CR幾何;非線型問題;ランダム行列;可換代数;一量子群;実特異点;ベクトル束;代数的組合せ論;量子群;可解モデル;非線形問題;代数的組合論;過剰決定系;複素解析, Algebraic;CR geometry;nonlinear problems;Combinatorics random matrix;Commutative Algebra;quantum group;real singularities;vector bundle
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06302001/

無限次元解析とその周辺の研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
山崎泰郎
From 01 Apr. 1993, To 31 Mar. 1994, Project Closed
無限次元解析;無限自由度物理系
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05640179/

代数構造の表現と組み合わせ論
Grant-in-Aid for General Scientific Research (B)
Kyoto University
三輪哲二
From 01 Apr. 1993, To 31 Mar. 1994, Project Closed
積分表示;qKZ方程式;S行列;量子展開環;D加群;ハイゼンベルグ表示;量子重力;位相的場の理論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05452004/

量子解析学の研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
荒木不二洋
From 01 Apr. 1992, To 31 Mar. 1993, Project Closed
量子解析学;量子重力;非調和振動子;接触多様体;カイラルポッツ模型;シルピンスキ・ガスケット
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04640155/

ガロア群、組み糸郡及び数論的関数の綜合的研究
Grant-in-Aid for General Scientific Research (B)
Kyoto University
伊原康隆
From 01 Apr. 1992, To 31 Mar. 1993, Project Closed
ガロア表現;代数曲線;基本群;組糸群;タイヒミュラー空間;量子群
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04452003/

無限自由度の可積分系の理論とその応用
Grant-in-Aid for Scientific Research on Priority Areas
Kyoto University
上野健爾
From 01 Apr. 1992, To 31 Mar. 1998, Project Closed
無限自由度;可積分系;可解格子模型;共形場理論;量子群;ミラー対称性;位相不変量;量子コホモロジー群;双対性;アフィンヘック環;写像類群;qKZ方程式;パンルベ方程式;3・4次元多様体;位相的場の理論;数論幾何学;無限自由度の可積分系;2次元格子模型;Calabi-Yau多様体;結晶基底;q類似;結び目;数論的多様体;ヤン・バクスター方程式
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04245108/

無限自由度の可積分系および無限次元代数
Grant-in-Aid for Scientific Research on Priority Areas
Kyoto University
三輪哲二
From 01 Apr. 1992, To 31 Mar. 1997, Project Closed
XXZ模型;ボゾン表示;オンサーガ-代数;非可換トーラス;マクドナルド多項式;非線型シグマ模型;アフィン量子群;アフィンヘッケ環;イジング模型;超対称性;サイン・ゴルドン理論;Macdonald多項式;モノドロミ-保存変形;パンルベVI型方程式;QKZ方程式;ミラー対称性;位相的ミニマル模型;非コンパクト型量子群;XXZスピン鎖;カジダン・ルスティッヒ予想;退化ヘッケ環;共形ブロック;スピン鎖;qKZ方程式;楕円的量子群;位相的場の理論;量子振幅;カラビ・ヤオ多様体;結晶基底;超幾何関数;可解格子模型;相関函数;量子群;チャーン・サイモン理論;ヤン・バクスター方程式;ベーテ仮説
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04245105/

ル-プ空間上の調和解析の総合的研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
楠岡成雄
From 01 Apr. 1991, To 31 Mar. 1992, Project Closed
ル-プ空間;調和解析;マリアバンカリキュラス
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03804006/

無限自由度の可積分系の理論とその応用ー幾何学・解析学の新展開ー
Grant-in-Aid for Co-operative Research (B)
Kyoto University
上野健爾
From 01 Apr. 1991, To 31 Mar. 1992, Project Closed
無限自由度の可積分系;共形場理論;可解格子模型;量子群;KP方程式系
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03352033/

Research on Fundamental Mathematical Sciences
Grant-in-Aid for Co-operative Research (A)
Nagoya University
Kazuhiko AOMOTO
From 01 Apr. 1991, To 31 Mar. 1994, Project Closed
数理科学;無限解析学;代数的組合せ論;量子解析学;情報科学;非線型解析;情報数理;モジュライ;基礎数理;無限次久力学系;非線形現象;散乱理論;カオス;無限解析;特殊微分方程式, Mathematical Sciences;Infinite Analysis;Algebraic Combinatories;Quantum Analysis;Information Science;Non-linear Analysis
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03302006/

マスタ-対称性の研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
荒木不二洋
From 01 Apr. 1990, To 31 Mar. 1991, Project Closed
マスタ-対称性;格子可解模型;正準作用素形式;超戸田格子階層;無限階微分方程式系;結晶基底
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640117/

無限自由度の解析学の総合的研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
三輪哲二
From 01 Apr. 1990, To 31 Mar. 1991, Project Closed
量子群;R行列;結晶基底;非調和振動子;自己双対アインシュタイン方程式;フックス群;ウィナ-空間;消滅定理
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640116/

Studies of D Module and Integrable System
Grant-in-Aid for General Scientific Research (B)
Kyoto University
Mikio SATO
From 01 Apr. 1990, To 31 Mar. 1992, Project Closed
超局所解析;WKB展開;Borel変換;結晶基底;Eichler積分;XY模型;定角曲線;Dー加群;非調和振動子;ボロス係数;量子群;R行列;ブレ-ド群;格子型模型;混合ホッジ加群, Micro-Local Analysis;WKB Method;Borel Transform;Crystal Base;Eichler Integral;XY Model;Constant Angle Curve;D Module
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02452009/

Studies of Algebraic and Analytic Varieties
Grant-in-Aid for General Scientific Research (B)
Kyoto University
Kyoji SAITO
From 01 Apr. 1990, To 31 Mar. 1992, Project Closed
Teichmuller空間;modular函数;量子群;vertex模型;K3曲面;Hodge加群;WKB理論;BRS cohomology;moduli空間;Teichmu^^¨ller空間;configuration空間;数理物理学;Hodge構造;L^2ーcohomology, Teichmuller Space;Modular Function;Quantum Group;Vertex Operator;K3 Surface;Hodge Module;WKB Theory;BRS Cohomology
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02452003/

Dynkin数学の綜合的研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
荒木不二洋
From 01 Apr. 1989, To 31 Mar. 1990, Project Closed
マスタ-対称性;XY模型;統計力学;可解模型;超リ-環;量子群
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540128/

Study of Infinite Dimensional Analysis and its Application.
Grant-in-Aid for General Scientific Research (C)
Kyoto University
Yasuo YAMASAKI
From 01 Apr. 1989, To 31 Mar. 1991, Project Closed
無限次元測度;確率過程;表現論;場の量子論;統計力学, Infinite dimensional measure.;Stochastic process.;Representation theory.;Quantum field theory;Statistic mechanics
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540127/

Noncommutative Analysis
Grant-in-Aid for Overseas Scientific Survey.
Research Institute for Mathematical Sciences, Kyoto University
Huzihiro ARAKI
From 01 Apr. 1989, To 31 Mar. 1990, Project Closed
非可換解析学;マスタ-対称性;量子群;色付き向きづけられたグラフ;テンソル積;カジュダン・ルスティッヒ予想;旗多様体;カッツ・ム-ディ-・リ-環, Non-commutative analysis;Master symmetries;Q-analogue;Colored oriented graph;Tensor product;Kazhdan-Lusztig conjecture;Flag variety;Kac-Moody Lie algebra
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01044073/

多様体をめぐる幾何学的諸問題の研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
島田信夫
From 01 Apr. 1988, To 31 Mar. 1989, Project Closed
孤立特異点;ルーと系とWeyl群;代数群の表現;Dー加群;無限次元グラスマン多様体;無限ループ空間;同変ホモトピー論;複素コボルディズム論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540036/

Studies of Algebraic Analysis
Grant-in-Aid for General Scientific Research (B)
Kyoto University
Masaki KASHIWARA
From 01 Apr. 1988, To 31 Mar. 1991, Project Closed
カッツ・ム-ディ-リ-環;量子群;可解格子模型;R行列;カイラル・ポッツ模型;ホッジ理論;非調和振動子;量子動;量子重力;無限次元多様体;結晶基底;共形場の理論;混合ホッジ加群;代数解析学;無限次元グラスマン多様体;無限次元リー環;共変量子力学, Kac-Moody algebra;Quantum group;Solvable lattice model;R matrix;Chiral Potts model;Hodge theory;unnarmonic oscillator;quantum gravity
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63460005/

無限次元測度の総合的研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
山崎泰郎
From 01 Apr. 1987, To 31 Mar. 1988, Project Closed
無限次元空間;測度;確率過程;汎関数解析;無限自由度の物理系;無限次元群;表現論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540108/

幾何学的構造に関する諸問題
Grant-in-Aid for General Scientific Research (C)
Kyoto University
島田信夫
From 01 Apr. 1987, To 31 Mar. 1988, Project Closed
モヂュライ空間;孤立特異点;代数解析;場の理論;アファインリー環;線型微分方程式;無限ループ空間;代数的K理論
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540042/

多様体の幾何学と関連分野の研究
Grant-in-Aid for General Scientific Research (C)
Kyoto University
島田信夫
From 01 Apr. 1986, To 31 Mar. 1987, Project Closed
複素コボルディズム;代数的K-理論;孤立特異点;代数曲面;複素多様体;代数解析;場の理論;偏微方程式
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540034/

Period map for primitive forms and their associated root systems and Lie algebras
Grant-in-Aid for Scientific Research (B)
Basic Section 11010:Algebra-related
Kyoto University
斎藤恭司
From 01 Apr. 2023, To 31 Mar. 2028, Granted
primitive form;periods;elliptic root system;highest weight modules;higher homotopy groups
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23H01068/

Representation theory and Algebraic analysis
Grant-in-Aid for Scientific Research (B)
Basic Section 11010:Algebra-related
Kyoto University
柏原正樹
From 01 Apr. 2020, To 31 Mar. 2025, Granted
代数解析;リーマン・ヒルベルト対応;モノイダル圏化;アフィン量子群;アフィンヘッケ箙圏;表現論;箙ヘッケ環;不確定特異点ホロノミック系;クラスター代数;圏化;量子群
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K20206/

Root systems and Lie algebras associated with period maps for primitive forms
Grant-in-Aid for Scientific Research (B)
Basic Section 11010:Algebra-related
Kyoto University
斎藤恭司
From 01 Apr. 2023, To 31 Mar. 2028, Granted
原始型式;周期写像と周期領域;一般化ルート系;可積分系;周期領域のホモトピー型;primitive form;periods;elliptic root system;highest weight modules;higher homotopy groups
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K25765/

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Kashiwara, Masaki

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