The Deligne-Simpson problem – a survey
نویسنده
چکیده
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) or cj ⊂ gl(n,C) so that there exist irreducible (resp. with trivial centralizer) (p + 1)-tuples of matrices Mj ∈ Cj or Aj ∈ cj satisfying the equality M1 . . .Mp+1 = I or A1+ . . .+Ap+1 = 0. The matrices Mj and Aj 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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