| Project/Area Number |
15540014
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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 | Ochanomizu University |
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Principal Investigator |
TAKEBE Takashi Ochanomizu University, Department of Mathematics, Associate Professor, 理学部, 助教授 (60240727)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | WZW model / elliptic curves / twisted WZW model / orbifold WZW model / Rational Conformal Field Theory / Separation of Variables / Loewner equation / twisted WZW model / 楕円曲線の退化 / conformal blockの分解 |
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| Research Abstract |
I studied the "twisted WZW model", which is a non-standard WZW model on elliptic curves. The factorisation theorem, which states that the sheaf of conformal blocks is locally free even at the boundary of the moduli space where the elliptic curve degenerates to a singular rational curve, has been proved. The sheaf of conformal blocks becomes that of the orbifold WZW model.
In particular, if one inserts integrable representations to marked points on the elliptic curve, this model gives another example of the rational conformal field theory.
I studied the following related topics, too :
1.Construction and generalisation of an integrable system on the monopole moduli space (a space of rational functions). Separation of variables of this system.
2.Relation of the Lowner equations and dispersionless integrable systems, in view of the boundary conformal field theory.
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