Semigroups of \(sl_3(\mathbb C)\) tensor product invariants (Q405822)

The authors give a presentation for the affine semigroup \(Q_{\mathcal{T}}(\mathfrak{sl}_3)\) formed by certain Berenstein-Zelevinsky triangles which appear in the problem of determining the decomposition of the \(\mathfrak{sl}_3\)-invariants in a tensor product of \(\mathfrak{sl}_3\)-modules. It turns out that the minimal generators for this semigroup correspond to certain subtrees of \(\mathcal{T}\) and all defining relations are either quadratic or cubic.NEWLINENEWLINEAs a bonus the authors find a new toric degeneration of the Grassmannian which are invariant for the diagonal torus.