| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
We have derived difference equations of KZ type for the correlation functions or the trace of the products of intertwining operators of the quantum toroidal algebra of type gl_1. We also investigated the structure of solutions and clarified the relation to the Nekrasov partition function of elliptic type. We have investigated the non-stationary difference equation for the K-theoretic Nekrasov partition function with a surface defect, which we can regard as a conformal block of the deformed Virasoro algebra. We have proved that by gauge
transformation the equation is transformed to a quantized version of discrete Painreve VI equation. The underlying moduli space is the affine Laumon space, which is only Kaehler quotient. In this sense this equation belongs to a new class of difference equations which was not expected in the beginning of the project.
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