| Project/Area Number |
14540025
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
NAGATOMO Kiyokazu Osaka University, Graduate School of Information Science and Technology, Associate Professor, 大学院・情報科学研究科, 助教授 (90172543)
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| Co-Investigator(Kenkyū-buntansha) |
YAMANE Hiroyuki Osaka University, Information Science and Technology, Associate Professor, 大学院・情報科学研究科, 助教授 (10230517)
KAWANAKA Noriaki Osaka University, Information Science and Technology, Professor, 大学院・情報科学研究科, 教授 (10028219)
MATSUMURA Akitaka Osaka University, Information Science and Technology, Professor, 大学院・情報科学研究科, 教授 (60115938)
WAKUI Michihisa Osaka University, Science, Assistant, 大学院・理学研究科, 助手 (60252574)
OHYAMA Yousuke Osaka University, Information Science and Technology, Associate Professor, 大学院・情報科学研究科, 助教授 (10221839)
伊達 悦朗 大阪大学, 大学院・情報科学研究科, 教授 (00107062)
坂根 由昌 大阪大学, 大学院・情報科学研究科, 教授 (00089872)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2002: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | conformal field theory / algebraic geometry / representation theory / vertex operator / vertex algebra / mathematical physics / 数理物理 / 共形ブロック / モジュラー変換 / リーマン面 |
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| Research Abstract |
We have formulated conformal field theory over genus one compact curve by establishing notions of sheaves of coinvariants and sheaves of conformal blocks, and have studied their mathematical structures. One of our tools to analyze these objects is the deformation theory of elliptic curve including the degenerate case. In fact we have used the structure theory of the space of meromorphic functions over elliptic curves with possible singularities only at the origin. The first step of our research is a canonical construction of connections defined on sheaves of coinvariants. These connections describe the dependence of sheaves on the deformation parameter of elliptic curves. Then Weierstrass' zeta function naturally appears as one of key ingredients in this construction. One of the most important problems is the construction of horizontal sections of sheaves of conformal blocks. We also have used the deformation theory to solve the differential equations and we have found that any solutions can be obtained from linear functional over an algebra which is associated to a vertex operator algebra. Consequently we are able to express any horizontal section in terms of traces of the finite-dimensional algebra. More generally there is a one to one correspondence between the space of horizontal sections and. the space of linear functional over the algebra.
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