A minimal Gröbner basis for simple ${\mathfrak{s}\mathfrak{l}}_n$- or ${\mathfrak{s}\mathfrak{p}}_n$-modules

We explicitly provide minimal Gröbner bases for simple, finite-dimensional modules of complex Lie algebras of types A and C, using a homogeneous ordering that is compatible with the PBW filtration on the universal enveloping algebras.