Abstract
The Deligne–Simpson problem (DSP) (respectively the weak DSP) is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes C j ⊂ GL ( n , C ) or c j ⊂ gl ( n , C ) so that there exist irreducible ( respectively with trivial centralizer) ( p + 1 ) -tuples of matrices M j ∈ C j or A j ∈ c j satisfying the equality M 1 ⋯ M p + 1 = I or A 1 + ⋯ + A p + 1 = 0 . The matrices M j and A j are interpreted as monodromy operators of regular linear systems and as matrices-residua of Fuchsian ones on Riemann's sphere. The present paper offers a survey of the results known up to now concerning the DSP.
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