supported by the Samsung Science and Technology Foundation(Grant No. SSTF-BA1602-03);supported by the National Research Foundation of Korea (Grant No. NRF-2019R1F1A1058962);supported by National Natural Science Foundation of China (Grant Nos. 11771455, 11822113 and 11831017);Guangdong Introducing Innovative and Enterpreneurial Teams (Grant No. 2017ZT07X355)。
We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety F?_(n1,...,nk;n) via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimens...
supported by National Natural Science Foundation of China(Grant Nos.11971250 and 12071320);Sichuan Science and Technology Program(Grant No.2020YJ0006)。
Let w be a permutation of{1,2,...,n},and let D(w)be the Rothe diagram of w.The Schubert polynomial■w_(x)can be realized as the dual character of the flagged Weyl module associated with D(w).This implies the following...
supported by National Center for Mathematics and Interdisciplinary Sciences,CAS。
In§13 of Schubert’s famous book on enumerative geometry,he provided a few formulas called coincidence formulas,which deal with coincidence points where a pair of points coincide.These formulas play an important role...
The research was supported by the National Natural Science Foundation of China(No.11525102).
Let l and n be positive integers such that l≥n,and let Gn,l be the Grassmannian which consists of the set of n-dimensionsil subspaces of C^(l),There is a Z-graded algebra isomorphism between the cohomology H*(Gn,l,Z)...
By applying a Grobner-Shirshov basis of the symmetric group Sn, we give two formulas for Schubert polynomials, either of which involves only nonnegative monomials. We also prove some combinatorial properties of Schube...