Richardson Varieties in a Toric Degeneration of the Flag Variety.

flag variety;Richardson variety;Groebner degeneration;Standard Monomial Theory;toric variety;Mathematics;Science;Mathematics

Kim, GiwanSmith, Karen E. ;

University of Michigan

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

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/113475/giwankim_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.