Geodesic
Some Examples of Rigid Representations
Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 253-276

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Consider the Deligne-Simpson problem: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) (resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp. A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann’s sphere. We give new examples of existence of such (p+1)-tuples of matrices Mj (resp. Aj ) which are rigid, i.e. unique up to conjugacy once the classes Cj (resp. cj) are fixed. For rigid representations the sum of the dimensions of the classes Cj (resp. cj) equals 2n^2 − 2.
Keywords: Monodromy Group, Rigid Representation 
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     author = {Kostov, Vladimir},
     title = {Some {Examples} of {Rigid} {Representations}},
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Kostov, Vladimir. Some Examples of Rigid Representations. Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 253-276. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_3_a5/