Degenerate Schubert Varieties in Type A

We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular element is indeed a Schubert variety in a partial flag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated to a rectangular element is isomorphic to the Demazure module for this particular Schubert variety of larger rank. This generalizes previous results by Cerulli Irelli, Lanini and Littelmann for the PBW degenerate flag variety.