Some examples related to the Deligne-Simpson problem

Vladimir Petrov Kostov

Some examples related to the Deligne-Simpson problem

Algebraic Geometry 2007-05-23 v1

Authors: Vladimir Petrov Kostov

Abstract

We consider the variety of $(p+1)$ -tuples of matrices $M_j$ from given conjugacy classes from $GL(n,{\bf C})$ such that $M_1... M_{p+1}=I$ . This variety is connected with the Deligne-Simpson problem and the matrices $M_j$ are interpreted as monodromy operators of regular systems on Riemann's sphere. We consider among others cases when the dimension of the variety is higher than the expected one due to the presence of $(p+1)$ -tuples with non-trivial centralizers.

Keywords

hadamard matrices operator theory painlevé equations

Cite

@article{arxiv.math/0011015,
  title  = {Some examples related to the Deligne-Simpson problem},
  author = {Vladimir Petrov Kostov},
  journal= {arXiv preprint arXiv:math/0011015},
  year   = {2007}
}

Comments

To appear in the proceedings of the Second International Confer ence on Geometry, Integrability and Quantization

Some examples related to the Deligne-Simpson problem

Abstract

Keywords

Cite

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