Difference analogues for conformal towers and the Ding-Iohara algebra
Project/Area Number |
24540206
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Global analysis
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Research Institution | The University of Tokyo |
Principal Investigator |
SHIRAISHI Junichi 東京大学, 数理(科)学研究科(研究院), 准教授 (20272536)
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Project Period (FY) |
2012-04-01 – 2015-03-31
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Project Status |
Completed (Fiscal Year 2014)
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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)
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Keywords | Macdonald多項式 / Askey-Wilson多項式 / Koornwinder多項式 / Ding-Iohara代数 / topological vertex / Laumon空間 / 共形場の理論 / 楕円超幾何級数 / Laumon space / Ruijsenaars作用素 / Nekrasov分配関数 / Whittaker関数 |
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).
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Report
(4 results)
Research Products
(10 results)
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[Presentation] On Askey-Wilson polynomials2013
Author(s)
Jun’ichi Shiraishi
Organizer
Representation Theory and applications to Combinatorics, Geometry and Quantum Physics, International Conference dedicated to the 60-th birthday of Boris Feigin
Place of Presentation
Higher School of Economics, Independent University of Moscow, Russia
Related Report
Invited
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