Macdonald polynomials, multivariable hypergeometric series and their application to lattice models
| Project/Area Number |
20540203
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 可能積分系 / マクドナルド多項式 / 超幾何級数 / Ding-Iohara代数 / topological vertex / Nekrasov分配関数 / 可積分系 / Din-Iohara代数 / 変形W代数 / Koornwinder多項式 / 可解格子模型 / 楕円量子群 / Macdonald多項式 / フュージョン則 |
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| Research Abstract |
I studied the representation theory of the Ding-Iohara algebra, clarifying a deep connection with the Macdonald polynomials. It was found that certain matrix elements of the homomorphisms of Ding-Iohara (or deformed Virasoro/W) algebra can be written as multivariable hypergeometric series, and are eigenfunctions of the Macdoanld difference operator. The series have a duality between the coordinate variables and momentum ones. For the Macdonald polynomials of type D and C, with one row partitions, similar hypergeometric series expressions are obtained by using the deformed W algebras.
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Report
(6 results)
Research Products
(40 results)
