5 problems

Let $L$ be a tensor product of irreducible finite-dimensional representations of $sl_{N+1}(\mathbb{C})$, marked by complex parameters $z=(z_1,\ldots,z_n)$. A Bethe vector is a vect…

Let $V_{\boldsymbol{\Lambda}}=V_{\boldsymbol{\Lambda}^1}\otimes\dots\otimes V_{\boldsymbol{\Lambda}^k}$ be the tensor product of the relevant $\mathfrak g$-modules. Let $z^0$ have…

Let $z=(z_1,\dots,z_n)$ be the parameters appearing in the master function … The corresponding Gaudin Hamiltonians act on the relevant representation space associated with the Gaud…

Transversality conjecture. For generic $z$, the intersection $\mathcal{I}_{\{\mathbf w\}}(z)$ is transversal and consists only of nondegenerate $p$-planes. In particular, for gener…

Let the master function associated with the inhomogeneous Gaudin model have critical points, considered modulo the relevant symmetry so that they form orbits, and let the correspon…