2010 Fiscal Year Final Research Report
Representations of double affine Hecke algebras and their applications to integrable systems
| Project/Area Number |
21740005
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KASATANI Masahiro The University of Tokyo, 大学院・数理科学研究科, 特任助教 (40527884)
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| Project Period (FY) |
2009 – 2010
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| Keywords | アフィンヘッケ環 / qKZ方程式 / Macdonald多項式 / Koornwinder多項式 |
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| Research Abstract |
(1) We formulated boundary qKZ equation in terms of the polynomial representation of the double affine Hecke algebra (DAHA) of type C^∨C. We gave a procedure to construct its polynomial solutions from solutions for an eigenvalue problem. Some special solutions are constructed by non-symmetric Koornwinder polynomials. (2) We confirmed that it will be possible to formulate a construction of polynomial solutions for a degenerate limit of the qKZ equation (with no boundary) in terms of the polynomial representation of degenerate DAHA. (3) We suggest an equality between non-symmetric Macdonald polynomials at roots of unity and Schur symmetric polynomials.
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