On solutions of the Schlesinger equations in terms of theta-functions
On solutions of the Schlesinger equations in terms of theta-functions
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施莱辛格方程的 theta 函数解
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
D. Korotkin
中科院分区：
文献类型：
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作者：
A. V. Kitaev;D. Korotkin
Schlesinger方程(见[18])产生于下面的黎曼-希尔伯特(逆单调)问题：对于任意g∈N和不同的2g+2点λj∈C，构造一个函数Ψ(λ)：Cp1{λ1，.。。，λ2g+2}→SL(2，C)具有如下性质：(1)Ψ(∞)=I；(2)Ψ(λ)对所有λ∈CP1{λ1，.。。，λ2g+2}；(3)Ψ(λ)在λ=λj，j=1，.。。，2g+2，具有给定的单行矩阵，Mj∈SL(2，C)。在单行矩阵独立于参数λ1的情况下，。。。，λ2g+2，函数Ψ≡Ψ(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