  We study the closure of the graph of the birational map from a projective
space to a Grassmannian. We provide explicit description of the graph closure
and compute the fibers of the natural projection to the Grassmannian. We
construct embeddings of the graph closure to the projectivizations of certain
cyclic representations of a degenerate special linear Lie algebra and study
algebraic and combinatorial properties of these representations. In particular,
we describe monomial bases, generalizing the FFLV bases. The proof relies on
combinatorial properties of a new family of poset polytopes, which are of
independent interest. As a consequence we obtain flat toric degenerations of
the graph closure studied by Borovik, Sturmfels and Sverrisd\'ottir.
