Classification of Ding's Schubert Varieties: Finer Rook Equivalence
نویسندگان
چکیده
منابع مشابه
Classification of Ding’s Schubert Varieties: Finer Rook Equivalence
K. Ding studied a class of Schubert varieties Xλ in type A partial flag manifolds, indexed by integer partitions λ and in bijection with dominant permutations. He observed that the Schubert cell structure of Xλ is indexed by maximal rook placements on the Ferrers board Bλ, and that the integral cohomology groups H∗(Xλ; Z), H ∗(Xμ; Z) are additively isomorphic exactly when the Ferrers boards Bλ,...
متن کاملMultiplicities on Schubert Varieties
We calculate using Macaulay 2 the multiplicities of the most singular point on Schubert varieties on Gl(n)/B for n = 5, 6. The method of computation is described and tables of the results are included.
متن کاملLarge Schubert Varieties
For a semisimple adjoint algebraic group G and a Borel subgroup B, consider the double classes BwB in G and their closures in the canonical compactification of G; we call these closures large Schubert varieties. We show that these varieties are normal and Cohen-Macaulay; we describe their Picard group and the spaces of sections of their line bundles. As an application, we construct geometricall...
متن کاملRook Poset Equivalence of Ferrers Boards
A natural construction due to K. Ding yields Schubert varieties from Ferrers boards. The poset structure of the Schubert cells in these varieties is equal to the poset of maximal rook placements on the Ferrers board under the Bruhat order. We determine when two Ferrers boards have isomorphic rook posets. Equivalently, we give an exact categorization of when two Ding Schubert varieties have iden...
متن کاملPermutation Representations on Schubert Varieties
This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t1, t2, . . . , tn]. We show these group actions are the same as an action studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and ot...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2007
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2007-002-9