# Some Examples of Rigid Representations

Serdica Mathematical Journal (2000)

- Volume: 26, Issue: 3, page 253-276
- ISSN: 1310-6600

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topKostov, Vladimir. "Some Examples of Rigid Representations." Serdica Mathematical Journal 26.3 (2000): 253-276. <http://eudml.org/doc/11493>.

@article{Kostov2000,

abstract = {*Research partially supported by INTAS grant 97-1644.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.},

author = {Kostov, Vladimir},

journal = {Serdica Mathematical Journal},

keywords = {Monodromy Group; Rigid Representation; monodromy group; rigid representation; matrix equations; Deligne-Simpson problem; conjugacy classes; Fuchsian systems; linear differential equations},

language = {eng},

number = {3},

pages = {253-276},

publisher = {Institute of Mathematics and Informatics},

title = {Some Examples of Rigid Representations},

url = {http://eudml.org/doc/11493},

volume = {26},

year = {2000},

}

TY - JOUR

AU - Kostov, Vladimir

TI - Some Examples of Rigid Representations

JO - Serdica Mathematical Journal

PY - 2000

PB - Institute of Mathematics and Informatics

VL - 26

IS - 3

SP - 253

EP - 276

AB - *Research partially supported by INTAS grant 97-1644.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.

LA - eng

KW - Monodromy Group; Rigid Representation; monodromy group; rigid representation; matrix equations; Deligne-Simpson problem; conjugacy classes; Fuchsian systems; linear differential equations

UR - http://eudml.org/doc/11493

ER -

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