Additive Deligne-Simpson problem was partially prooved by Kostov. Also there is Crawley-Boevey's approach to the question. The problem is about existence of a solution of the equation $$ A_1 +...+A_n = 0, $$ where $A_i \in \mathcal{O}_i$, and $\mathcal{O}_i$ is a fixed coadjoint orbit in $\mathfrak{gl}_r$. How the land lies in the case of other classical groups such as orthogonal or symplectic?
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