Analysis of the solution space for the quantum KZ equation and its applications to integrable systems
Project/Area Number |
23740119
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Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Global analysis
|
Research Institution | University of Tsukuba |
Principal Investigator |
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 可積分系 / 多重ゼータ値 / 差分方程式 / 量子KZ方程式 / 二重アフィンヘッケ代数 |
Research Abstract |
We get two results about related problems to the quantum Knizhnik-Zamolodchikov equation. First, we constructed an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. A family of linear relations called the double shuffle relations is formulated and proved in our framework. Second, we defined a discrete analogue of the Hamiltonian of the non-ideal Bose gas with delta-potentials, and constructed eigenfunctions by means of the Bethe ansatz method making use of a representation of the affine Hecke algebra.
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Report
(4 results)
Research Products
(11 results)