On the Deligne-Simpson problem
| dc.creator | Kostov, Vladimir Petrov | |
| dc.date | 2000-11-02 | |
| dc.date.accessioned | 2026-07-07T04:38:25Z | |
| dc.date.available | 2026-07-07T04:38:25Z | |
| dc.description | The Deligne-Simpson problem is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset SL(n,{\bf C})$ or $c_j\subset sl(n,{\bf C})$ so that there exist irreducible $(p+1)$-tuples of matrices $M_j\in C_j$ or $A_j\in c_j$ satisfying the equality $M_1... M_{p+1}=I$ or $A_1+... +A_{p+1}=0$. We solve the problem for generic eigenvalues with the exception of the case of matrices $M_j$ when the greatest common divisor of the numbers $Σ_{j,l}(σ)$ of Jordan blocks of a given matrix $M_j$, with a given eigenvalue $σ$ and of a given size $l$ (taken over all $j$, $σ$, $l$) is $>1$. Generic eigenvalues are defined by explicit algebraic inequalities. For such eigenvalues there exist no reducible $(p+1)$-tuples. 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. | |
| dc.identifier | https://arxiv.org/abs/math/0011013 | |
| dc.identifier | http://arxiv.org/abs/math/0011013 | |
| dc.identifier | Proc. Steklov Inst. v. 238 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60272 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.title | On the Deligne-Simpson problem | |
| dc.type | text |