Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/420

 Title: Some Examples of Rigid Representations Authors: Kostov, Vladimir Keywords: Monodromy GroupRigid Representation Issue Date: 2000 Publisher: Institute of Mathematics and Informatics Citation: Serdica Mathematical Journal, Vol. 26, No 3, (2000), 253p-276p Abstract: 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. Description: *Research partially supported by INTAS grant 97-1644. URI: http://hdl.handle.net/10525/420 ISSN: 1310-6600 Appears in Collections: Volume 26 Number 3

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