Derived categories and infinite dimensional Lie algebras associated with primitive forms

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20340011
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: SAITO Kyoji The University of Tokyo, 数物連携宇宙研究機構, 特任教授 (20012445)
• Project Period (FY): 2008-04-08 – 2013-03-31
• Keywords: 原始形式の周期写像 / 無限次元リー環 / 熱力学的極限関数

Research Abstract

当研究計画の目的は大きくは次の二点から成る。
(1)原始形式をリー代数的に構成する為のリー代数のカテゴリカルな研究
(2)基本群などのモノイド等の構造の理解とそれに付随する統計力学的極限関数の構成の研究

Research Products

• [Journal Article] Limit elements in the Configuration Algebra for Cancellative Monoids (2010)
  • Author(s): K.Saito
  • Journal Title: Publication RIMS Kyoto Univ. 46, no.1 Pages: 37-113
  • Peer Reviewed
• [Journal Article] Growth functions for Artinmonoids (2009)
  • Author(s): K.Saito
  • Journal Title: Proceedings of Symposia in Pure Mathematics. Vol.85, No.7 Pages: 84-88
  • Peer Reviewed
• [Journal Article] Triangulated Categories of Matrix factorizations for Regular Systems of Weights with ε=-1 (2009)
  • Author(s): H.Kajiura, K.Saito, A.Takahashi
  • Journal Title: Advances in Math. 220, no.5 Pages: 1602-1654
  • Peer Reviewed
• [Journal Article] Towards a categorical construction of Lie algebras (2008)
  • Author(s): K.Saito
  • Journal Title: Adv.Stud.Pure Math. 50 Pages: 101-175
  • Peer Reviewed
• [Journal Article] Growth functions associated with Artin monoids of finite type. (2008)
  • Author(s): K.Saito
  • Journal Title: Proceedings of the Japan Academy Vol.84, Ser.A, No.10 Pages: 179-183
  • Peer Reviewed
• [Journal Article] From Primitive Forms to Frobenius manifolds (2008)
  • Author(s): K.Saito, A.Takahashi
  • Journal Title: Proceedings of the Japan Academy. Vol.84, Ser.A, No.10 Pages: 179-183
  • Peer Reviewed
• [Journal Article] Monoids in the fundamental groups of the complement of logarithmic free divisors in C^3
  • Author(s): T.Lshibe, K.Saito
  • Journal Title: Journal of Algebra. To appear
  • Peer Reviewed
• [Journal Article] Coxeter Elements of Vanishing Cycles of Types A_<1/2∞> and D_<1/2∞>
  • Author(s): K.Saito
  • Journal Title: Annales de d'Institut Fourier. To appear
  • Peer Reviewed
• [Journal Article] Opposite sequences
  • Author(s): K.Saito
  • Journal Title: European Journal of Combinatorics. To appear
  • Peer Reviewed
• [Presentation] F-functions associated with cancellative monoids. (2011)
  • Author(s): Kyoji Saito
  • Organizer: Long Term Workshop Geometry and Analysis, Japan-France Sakura-project.
  • Place of Presentation: Kyoto university, Kyoto Japan.
  • Year and Date: 2011-03-07
• [Presentation] The lattice of vanishing cyceles of types A_<1/2∞> and D_<1/2∞>. (2011)
  • Author(s): Kyoji Saito
  • Organizer: Conference on Derived Category.
  • Place of Presentation: the university of Tokyo, Tokyo, Japan.
  • Year and Date: 2011-01-26
• [Presentation] Spectral decomposition of the Coxeter elements of types A_<1/2∞> and D_<1/2∞> (2011)
  • Author(s): Kyoji Saito
  • Organizer: Japan-Vietnam bilateral program
  • Place of Presentation: Tohoku university
  • Year and Date: 2011-01-05
• [Presentation] Reflection groups of types A_<1/2∞> and D_<1/2∞>, Lattices. (2010)
  • Author(s): Kyoji Saito
  • Organizer: Reflection groups and Algebraic Geometry.
  • Place of Presentation: Nagoya university Japan.
  • Year and Date: 2010-11-26
• [Presentation] Singurarities of the transcendental functions of types A_<1/2∞> and D_<1/2∞>. (2010)
  • Author(s): Kyoji Saito
  • Organizer: Conference on Rreal Singurairties.
  • Place of Presentation: RIMS, Kyoto Japan.
  • Year and Date: 2010-11-01
• [Presentation] Limit partition functions associated with Cancellative monoids. (2010)
  • Author(s): Kyoji Saito
  • Organizer: Kinosaki symposium of Algebraic geometry.
  • Place of Presentation: Kinosak, Japan.
  • Year and Date: 2010-10-25
• [Presentation] Highest weight representation of Elliptic Lie Algebras. (2010)
  • Author(s): Kyoji Saito
  • Organizer: 4^<th> International Conference on Representation Thoery.
  • Place of Presentation: Xian, China.
  • Year and Date: 2010-08-13
• [Presentation] Primitive forms of types A_<1/2∞> and D_<1/2∞>. (2010)
  • Author(s): Kyoji Saito
  • Organizer: Conference on.
  • Place of Presentation: Grenoble, France.
  • Year and Date: 2010-06-04
• [Presentation] The lattice of vanishing cyceles of types A_<1/2∞> and D_<1/2∞>. (2010)
  • Author(s): Kyoji Saito
  • Organizer: Conference in honor of Claus Ringel and Kyoji Saito.
  • Place of Presentation: Xinhoa university, Beijing, China.
  • Year and Date: 2010-05-05