2011 Fiscal Year Final Research Report
Macdonald polynomials, multivariable hypergeometric series and their application to lattice models
| Project/Area Number |
20540203
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | 可能積分系 |
|---|
| 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.
|
Research Products
(20 results)
