5 problems

Kirillov's integrality conjecture. The polytopes $\mathrm{GT}_{\lambda,\beta}$ are integral polytopes.

Let $\mathcal{GT}_{\lambda,\mu}$ denote a Gelfand–Tsetlin polytope, with parameters $\lambda$ and $\mu$. Call a polytope Ehrhart positive when all coefficients of its Ehrhart polyn…

Vertex-preservation conjecture. The map $\phi_\lambda$ induces a bijection

Let $\mathcal{P}_{{\boldsymbol\lambda}/{\boldsymbol\mu},\mathbf{w}}$ be a weight-restricted Gelfand–Tsetlin polytope defined by a skew shape ${\boldsymbol\lambda}/{\boldsymbol\mu}$…

Let $\mathcal{P}_{{\boldsymbol\lambda}/{\boldsymbol\mu},\mathbf{w}}$ be a weight-restricted Gelfand–Tsetlin polytope defined by a skew shape ${\boldsymbol\lambda}/{\boldsymbol\mu}$…