On the existence of monodromy groups of Fuchsian systems on Riemann’s sphere with unipotent generators. (English) Zbl 0948.34066
Here, the following Deligne-Simpson problem is considered: For what choice of the \((p+1)\)-tuple of conjugacy classes \(C_1,\dots, C_{p+1}\) in \(\text{GL}(n,\mathbb{C})\), \(p\geq 2\), do there exist irreducible \((p+1)\)-tuples of matrices \(M_j\in C_j\) such that \(M_1,\dots, M_{p+1}= I\), \(I\) being the identity matrix? Necessary and sufficient conditions for the existence of such tuples in the case where \(M_j\) are unipotent are investigated.
Reviewer: S.K.Chatterjea (Calcutta)
MSC:
| 34M35 | Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms |
Keywords:
monodromy groups; Fuchsian systems; Riemann’s sphere; unipotent generators; Deligne-Simpson problemReferences:
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