| Project/Area Number |
26800004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyoto University (2015)
The University of Tokyo (2014) |
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Principal Investigator |
Ip Ivan 京都大学, 大学院理学研究科, 助教 (50646031)
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | Positive Representation / quantum groups / modular double / Teichmuller theory / braided tensor category / positive representation / TQFT / Casimir operators / Modular Double / Teichmuller Theory / cluster algebra / quantum Lie superalgebra |
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| Outline of Final Research Achievements |
We have showed that the restriction of positive representation to the Borel part is independent of the parameters λ and also closed under taking tensor product. We construct the quantum mutation operator as part of the candidate of the quantum higher Teichmuller theory. We studied the eigenvalues of the positive Casimir, and its relation to discriminant variety. We develop the idea of virtual highest weight and show that the Clebsch-Gordan coefficients for tensor product decomposition of Uq(sl(2,R)) are certain analytic continuation of the classical coefficients.
In joint works with A. Zeitlin, we studied the Baxter Q operator for Cq(2)(2) and calculate explicitly the R operators using the spinor trick developed for split real case. We also studied the generalization of decorated super Teichmuller space for N=2 with structure group OSp(2|2) Finally with M. Yamazaki, we generalize Bazhanov’s quantum dilogarithm identities in the root of unity limit.
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Report
(3 results)
Research Products
(12 results)
