Semigroups of sl3(C)sl3(C) tensor product invariants

We find presentations for a family of semigroup algebras related to the problem of decomposing sl3(C)sl3(C) tensor products. Along the way we find new toric degenerations of the Grassmannian variety Gr3(Cn)Gr3(Cn) which are T  -invariant for T⊂GLn(C)T⊂GLn(C) the diagonal torus.