On Solutions of the Schlesinger Equations in Terms of Θ-functions
On Solutions of the Schlesinger Equations in Terms of Θ-functions
复制标题
用 θ 函数解施莱辛格方程
DOI：
--
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Humboldt Foundation
中科院分区：
文献类型：
--
作者：
A. V. Kitaev;D. Korotkin;Alexander Von;Humboldt Foundation
Schlesinger方程（见[18]）出现在下面的Riemann-Hilbert（逆单值）问题的背景下：对于任意g ∈ N和不同的2g + 2点λj ∈ C，构造一个函数λ j（λ）：CP 1 {λ1，. . .，λ2g+2} → SL（2，C），它具有以下性质：（1）<$（∞）= I;（2）<$（λ）对所有λ ∈ CP 1 {λ1，. . .，λ2g+2};（3）λ（λ）在λ = λj，j = 1，. . .，2g + 2，对于给定的单值矩阵，Mj ∈ SL（2，C）.在单值矩阵与参数λ1，. . .，λ2g+2，函数λ_（？）（λ）解矩阵微分方程
The Schlesinger equations (see [18]) arise in the context of the following Riemann-Hilbert (inverse monodromy) problem: For an arbitrary g ∈ N and distinct 2g + 2 points λj ∈ C, construct a function Ψ(λ): CP1 {λ1, . . . , λ2g+2} → SL(2,C) which has the following properties: (1) Ψ(∞) = I; (2) Ψ(λ) is holomorphic for all λ ∈ CP1 {λ1, . . . , λ2g+2}; (3) Ψ(λ) has regular singular points at λ = λj, j = 1, . . . ,2g + 2, with given monodromy matrices, Mj ∈ SL(2,C). In the case where the monodromy matrices are independent of the parameters λ1, . . . , λ2g+2, the function Ψ ≡ Ψ(λ) solves the matrix differential equation