Representation theoretic research of Painleve systems
| Project/Area Number |
23540003
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
Kuroki Gen 東北大学, 理学(系)研究科(研究院), 助教 (10234593)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 量子パンルヴェ系 / 量子群 / カッツ・ムーディ代数 / ワイル群双有理作用 / ベックルント変換 / τ函数 / 共形場理論 / パンルヴェ方程式 |
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| Outline of Final Research Achievements |
We quantize the tau-functions generated by the birational action of the Weyl group associated to any symmetrizable generalized Cartan matix (GCM). For example, if the GCM is of the affine A_2 type, then the quantized tau-functions are identified with the ones for the quantum Painleve IV equation. The classical tau-functions are polynomials in independent variables. We establish the quantized version that the quantized tau-functions are non-commutative polynomials in the quantized independent variables. The proof is derived from the certain formulae of the translation functors in the BGG category for the Kac-Moody algebra. Using the theory of quantum groups, we can generalize these results to the cases of q-difference analogues.
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Report
(6 results)
Research Products
(6 results)
