On some aspects of the Deligne-Simpson problem

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dc.creatorKostov, Vladimir Petrov
dc.date2000-05-02
dc.date.accessioned2026-07-07T04:34:57Z
dc.date.available2026-07-07T04:34:57Z
dc.descriptionThe 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 $Σ_{j,m}(σ)$ of Jordan blocks of a given matrix $M_j$, with a given eigenvalue $σ$ and of a given size $m$ (taken over all $j$, $σ$, $m$) 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.
dc.descriptionTo appear in a volume of ``Trudy Seminara Arnol'da''
dc.identifierhttps://arxiv.org/abs/math/0005016
dc.identifierhttp://arxiv.org/abs/math/0005016
dc.identifierJournal of Dynamical and Control Systems, vol. 9, No. 3, July 2003, 393-436
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59106
dc.subjectAlgebraic Geometry
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.titleOn some aspects of the Deligne-Simpson problem
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