منابع مشابه
Symplectic Multiple Flag Varieties of Finite Type
Problem: Given a reductive algebraic group G, find all k-tuples of parabolic subgroups (P1, . . . , Pk) such that the product of flag varieties G/P1 × · · · ×G/Pk has finitely many orbits under the diagonal action of G. In this case we call G/P1× · · · ×G/Pk a multiple flag variety of finite type. In this paper, we solve this problem for the symplectic group G = Sp2n. We also give a complete en...
متن کاملSchubert Polynomials and Arakelov Theory of Symplectic Flag Varieties
Let X = Sp 2n/B the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of X. We use these polynomials to describe the arithmetic Schubert calculus on X. Moreover, we give a method to compute the natural arithmetic Chern numbers on X, and show that they ar...
متن کاملParametrizations of Flag Varieties
For the flag variety G/B of a reductive algebraic group G we define and describe explicitly a certain (set-theoretical) cross-section φ : G/B → G. The definition of φ depends only on a choice of reduced expression for the longest element w0 in the Weyl group W . It assigns to any gB a representative g ∈ G together with a factorization into simple root subgroups and simple reflections. The cross...
متن کاملCombinatorics in affine flag varieties
The Littelmann path model gives a realisation of the crystals of integrable representations of symmetrizable Kac-Moody Lie algebras. Recent work of Gaussent-Littelmann [GL] and others [BG] [GR] has demonstrated a connection between this model and the geometry of the loop Grassmanian. The alcove walk model is a version of the path model which is intimately connected to the combinatorics of the a...
متن کاملShelling Totally Nonnegative Flag Varieties
In this paper we study the partially ordered set Q of cells in Rietsch’s [20] cell decomposition of the totally nonnegative part of an arbitrary flag variety P ≥0 . Our goal is to understand the geometry of P ≥0 : Lusztig [13] has proved that this space is contractible, but it is unknown whether the closure of each cell is contractible, and whether P ≥0 is homeomorphic to a ball. The order comp...
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: 2014
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2013-038-6