On the weak Deligne-Simpson problem for index of rigidity 2

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dc.creatorKostov, Vladimir Petrov
dc.date2002-04-02
dc.date.accessioned2026-07-07T04:47:24Z
dc.date.available2026-07-07T04:47:24Z
dc.descriptionWe consider the weak version of the Deligne-Simpson problem: give necessary and sufficient conditions upon the conjugacy classes $c_j\subset gl(n,{\bf C})$ (resp. $C_j\subset GL(n,{\bf C})$) so that there exist $(p+1)$-tuples of matrices $A_j\in c_j$, $A_1+... +A_{p+1}=0$ (resp. $M_1... M_{p+1}=I$) with trivial centralizers (i.e. reduced to scalars). The true Deligne-Simpson problem requires irreducibility instead of triviality of the centralizer. When the eigenvalues are generic, a Criterium on the Jordan normal forms defined by the conjugacy classes gives the necessary and sufficient conditions for solvability of the true problem. For index of rigidity 2 (i.e. when the sum of the dimensions of the conjugacy classes equals $2n^2-2$) we show that for a sufficiently large class of $(p+1)$-tuples of conjugacy classes the answer to the weak problem is negative. These conjugacy classes define Jordan normal forms that satisfy the Criterium.
dc.descriptionSubmitted to the Proceedings of the Colloquium in the memory of Ruth Michler (Luminy 2001)
dc.identifierhttps://arxiv.org/abs/math/0204030
dc.identifierhttp://arxiv.org/abs/math/0204030
dc.identifierContemporary Mathematics 324 (2003), Topics in Algebraic Geometry and Noncommutative Geometry, C. G. Melles, J.-P. Brasselet, G. Kennedy, K. Lauter, L. McEvan Eds., 139-153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63699
dc.subjectAlgebraic Geometry
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.titleOn the weak Deligne-Simpson problem for index of rigidity 2
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