Richardson Varieties in a Toric Degeneration of the Flag Variety.

摘要

In this thesis, we study the degenerations of Richardson varieties in the Groebner degeneration of the flag variety into the toric variety of the Gelfand-Tsetlin polytope. Our result is that a Richardson variety degenerates into a reduced union of toric subvarieties corresponding to faces of the Gelfand-Tsetlin polytope parametrized by reduced pipe dreams. We apply Standard Monomial Theory to complete the line of reasoning in [Kogan-Miller '05] that relates the degeneration of a matrix Schubert variety [Knutson-Miller '05] to that of a Schubert variety.