現代数学の系譜工学物理雑談古典ガロア理論も読む78

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む78 (1002ﾚｽ)
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649: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/09(土) 06:49:24.66 ID:aIAMZK1h

>>607
>モノドロミーで、GL(n, C)が出てくるよ（＾＾

(参考)
https://ja.wikipedia.org/wiki/%E3%83%A2%E3%83%8E%E3%83%89%E3%83%AD%E3%83%9F%E3%83%BC
モノドロミー
脚注
2 ^ V.P. Kostov (2004), “The Deligne?Simpson problem ? a survey”, J. Algebra 281 (1): 83?108, doi:10.1016/j.jalgebra.2004.07.013, MR2091962 and the references therein.
V.P. Kostov / Journal of Algebra 281 (2004) 83?108
The Deligne?Simpson problem?a survey
Vladimir Petrov Kostov
Universite de Nice?Sophia Antipolis, Laboratoire de Mathematiques,
Parc Valrose, 06108 Nice cedex 2, France
Received 18 September 2002
Available online 3 September 2004
(抜粋)
1. Introduction
1.1. Regular and Fuchsian linear systems on Riemann’s sphere
The problem which is the subject of this paper admits a purely algebraic formulation.
Yet its importance lies in the analytic theory of systems of linear differential equations, this
is why we start by considering the linear system of ordinary differential equations defined
on Riemann’s sphere:
dX/dt = A(t)X. (1)
Here the n × n-matrix A is meromorphic on CP1, with poles at a1, . . . ,ap+1; the dependent
variables X form an n×n-matrix.Without loss of generality we assume that∞is not
among the poles aj and not a pole of the 1-form A(t) dt . In modern literature (see, e.g.,
[18]) the terminology of meromorphic connections and sections is often preferred to the
one of meromorphic linear systems and their solutions and there is a 1?1-correspondence
between the two languages.

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