2013 Fiscal Year Final Research Report
Derive categories and infinite dimensional Lie allgebras associated with primitive forms
| Project/Area Number |
20340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
SAITO Kyoji 東京大学, カブリ数物連携宇宙研究機構, 特任教授 (20012445)
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| Co-Investigator(Kenkyū-buntansha) |
KONO Toshitake 東京大学, 大学院数理科学研究科, 教授 (80144111)
JIMBO Michio 東京大学, 大学院数理科学研究科, 教授 (80109082)
KASHIWARA Masaki 京都大学, 数理解析研究所, 教授 (60027381)
TAKAHASHI Atsushi 大阪大学, 理学研究科, 准教授 (50314290)
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| Project Period (FY) |
2008-04-08 – 2013-03-31
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| Keywords | 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 |
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| Research Abstract |
The purpose of the program is the study is A. primitive forms, and B. thermodynamical limit functions for discrete groups.
A. Towards categorical construction of primitive forms, 1. we constructed the highest weight integrable representations of elliptic Lie algebras, and 2. we determine the strongly exceptional collections of the categories of matrix factorizations for simply elliptic and 14 exceptional unimodular singularities (joint work with Takahashi, Kajiura and Oda). On the other hand, We started the construction of primitive forms for the function of type A and D with infinite critical points.
B. We generalized the theory of the thermodynamical limit functions for a discrete group to any cancellative monoid. Then, the study of growth functions for cancellative monoids had big progress, and the inversion formula of the growth function is constructed in the monoid level. In particular, the monoid of integral square matrices shows a strong similarity with Artin monoids.
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