Quantum Kostka and the rank one problem for \(\mathfrak{sl}_{2m}\) (Q1737115)

The author describes how to specify vector bundles of conformal blocks for $\mathfrak{sl}_{2M}$ with rectangular weights of ranks $0$, $1$, and larger than $1$, respectively. For rank one bundles, the author further shows that their first Chern classes determine a finitely generated subcone of the nef cone of the moduli space of stable $n$-pointed rational curves. In order to prove the results, the author uses Witten's dictionary and Kostka numbers for computing ranks by counting Young tableaux.