4 problems

Quantum complete integrability conjecture. There exists $\kappa=\kappa(N,d)>0$ such that

Higher-Hamiltonian eigenvalue conjecture.

Conjectural action of $X^{(1)}_{\pm1}$.

Let $T^{(1)}_{ij}[0]$ be the partial zero modes in a ${\rm GL}(N)$-invariant model. Bethe vectors and dual Bethe vectors are parametrized by sets $\bar t^k$ and cardinalities $a_k$…