| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Outline of Final Research Achievements |
A quantum group approach to the refined topological vertex of Iqbal-Kozcaz-Vafa is presented in terms of the Ding-Iohara algebra (joint work with H. Awata and B. Feigin).
A four-fold series expression is obtained for the Askey-Wilson polynomial. It gives us an explicit formula for the Koornwinder polynomials in one row case. Lassalle's conjectures for the Macdonald polynomials for types B,C,D are recovered, hence proved, as special cases of the formula for the Koornwinder polynomials (joint work with A. Hoshino and M. Noumi).
A geometric construction is presented for the Macdonald polynomials of A-type as the Euler characteristic of the twisted de Rham complex for the Laumon space. The Macdonald polynomials of other types can be considered in some other algebro-geometric setting, and a conjecture aout a geometric construction is given (joint work with A. Braverman and M. Finkelberg).
|
