The Deligne-Simpson problem -- a survey

Vladimir Petrov Kostov

The Deligne-Simpson problem -- a survey

环与代数 2007-05-23 v1 代数几何表示论

作者: Vladimir Petrov Kostov

摘要

The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there exist irreducible (resp. with trivial centralizer) $(p+1)$ -tuples of matrices $M_j\in C_j$ or $A_j\in c_j$ 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.

关键词

hadamard matrices partial differential equations painlevé equations

引用

@article{arxiv.math/0206298,
  title  = {The Deligne-Simpson problem -- a survey},
  author = {Vladimir Petrov Kostov},
  journal= {arXiv preprint arXiv:math/0206298},
  year   = {2007}
}

The Deligne-Simpson problem -- a survey

摘要

关键词

引用

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