2012 Fiscal Year Final Research Report
Representations of the quantum groups at roots of unity and its application to knot theory
| Project/Area Number |
22540236
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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 |
Global analysis
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| Research Institution | Waseda University |
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Principal Investigator |
MURAKAMI Jun 早稲田大学, 理工学術院, 教授 (90157751)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 可積分系 / 量子群 / 量子不変量 / 位相幾何学 / 作用素環 |
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| Research Abstract |
We did research rerated to the ‘Volume Conjecture’ which gives a relation between the quantum invariant related to the quantum group Uq(sl2), and, by noticing the non-semisimple representation of it, such representations and the related knot invariants were studied. By applying the volume conjecture, the geometric structure of a knot complement and the volumes of polyhedrons in a three space with a constant curvature were studied. Moreover, new invariants of knots in a three manifolds were constructed from the non-semisimple representations.
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