Vertex operator construction of standard modules for \(A_ n^{(1)}\) (Q1318485)

We generalize the vertex operator formula for the affine Lie algebra \(A_ n^{(1)}\) in the ``homogeneous picture'' and by using it we construct a basis of any given standard \(A_ n^{(1)}\)-module parametrized by coloured partitions. We also obtain a similar explicit construction of vacuum spaces of standard \(A_ 2^{(1)}\)-modules.