2013 Fiscal Year Final Research Report
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)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 可積分系 |
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| 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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