On some aspects of the Deligne-Simpson problem

Details On some aspects of the Deligne-Simpson problem On some aspects of the Deligne-Simpson problem

2000-05-02

arxiv.org/abs/math/0005016v1

Journal of Dynamical and Control Systems, vol. 9, No. 3, July 2003, 393-436

Mathematics

Algebraic Geometry

To appear in a volume of ``Trudy Seminara Arnol'da''

Scientific paper

The Deligne-Simpson problem in the multiplicative version is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\in SL(n,{\bf C})$ so that there exist irreducible $(p+1)$-tuples of matrices $M_j\in C_j$ satisfying the equality $M_1... M_{p+1}=I$}. We solve the problem for generic eigenvalues in the case when all the numbers $\Sigma_{j,m}(\sigma)$ of Jordan blocks of a given matrix $M_j$, with a given eigenvalue $\sigma$ and of a given size $m$ (taken over all $j$, $\sigma$, $m$) are divisible by $d>1$. Generic eigenvalues are defined by explicit algebraic inequalities of the form $a\neq 0$. For such eigenvalues there exist no reducible $(p+1)$-tuples. The matrices $M_j$ are interpreted as monodromy operators of regular linear systems on Riemann's sphere.

Affiliated with

Also associated with

No associations

Rating

On some aspects of the Deligne-Simpson problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On some aspects of the Deligne-Simpson problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some aspects of the Deligne-Simpson problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-98466