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過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 担当者 | 大島 利雄, 坂井 秀隆 |
|---|
2014年03月19日(水)
16:00-17:00 数理科学研究科棟(駒場) 128号室
Anton Dzhamay 氏 (University of Northern Colorado)
Discrete Schlesinger Equations and Difference Painlevé Equations (ENGLISH)
Anton Dzhamay 氏 (University of Northern Colorado)
Discrete Schlesinger Equations and Difference Painlevé Equations (ENGLISH)
[ 講演概要 ]
The theory of Schlesinger equations describing isomonodromic
dynamic on the space of matrix coefficients of a Fuchsian system
w.r.t.~continuous deformations is well-know. In this talk we consider
a discrete version of this theory. Discrete analogues of Schlesinger
deformations are Schlesinger transformations that shift the eigenvalues
of the coefficient matrices by integers. By discrete Schlesinger equations
we mean the evolution equations on the matrix coefficients describing
such transformations. We derive these equations, show how they can be
split into the evolution equations on the space of eigenvectors of the
coefficient matrices, and explain how to write the latter equations in
the discrete Hamiltonian form. We also consider some reductions of those
equations to the difference Painlevé equations, again in complete parallel
to the differential case.
This is a joint work with H. Sakai (the University of Tokyo) and
T.Takenawa (Tokyo Institute of Marine Science and Technology).
The theory of Schlesinger equations describing isomonodromic
dynamic on the space of matrix coefficients of a Fuchsian system
w.r.t.~continuous deformations is well-know. In this talk we consider
a discrete version of this theory. Discrete analogues of Schlesinger
deformations are Schlesinger transformations that shift the eigenvalues
of the coefficient matrices by integers. By discrete Schlesinger equations
we mean the evolution equations on the matrix coefficients describing
such transformations. We derive these equations, show how they can be
split into the evolution equations on the space of eigenvectors of the
coefficient matrices, and explain how to write the latter equations in
the discrete Hamiltonian form. We also consider some reductions of those
equations to the difference Painlevé equations, again in complete parallel
to the differential case.
This is a joint work with H. Sakai (the University of Tokyo) and
T.Takenawa (Tokyo Institute of Marine Science and Technology).
