5 problems

Horn's conjecture. The inequalities arising from the recursively characterized triples $(I,J,K)$ are sufficient to characterize all Horn triples $(\lambda,\mu,\nu)$; equivalently,…

Tropical multiple Horn conjecture. For sufficiently large networks $\Pi_1,\Pi_2,\Pi_3$, for example standard networks, these conditions are necessary and sufficient. Equivalently,…

Multiplicative multiple Horn conjecture. For every $\varepsilon>0$, there exists $s_0>0$ such that, for every $s>s_0$,

Planar-network multiple Horn conjecture. For sufficiently large planar networks, these conditions are also sufficient for $(\lambda, \mu, \nu, \rho, \sigma, \tau)$ to be realized a…

Let $V_{\boldsymbol{a}}$, $V_{\boldsymbol{b}}$, and $V_{\boldsymbol{c}}$ be irreducible representations of $\mathcal{U}(N)$ indexed by…