Richardson Varieties in a Toric Degeneration of the Flag Variety.

[摘要] In this thesis, we study 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.

[发布机构] University of Michigan

[效力级别] Richardson variety

[关键词] flag variety;Richardson variety;Groebner degeneration;Standard Monomial Theory;toric variety;Mathematics;Science;Mathematics