Parametrizations of flag varieties
نویسندگان
چکیده
منابع مشابه
Parametrizations 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...
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This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal rational parametrizations of certain projective varieties. We give numerous examples and then discuss what happens in the singular case. We also describe rational ...
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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...
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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...
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We show that the Borel-equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of dg modules over the extension algebra of the direct sum of the simple equivariant perverse sheaves. This proves a conjecture of Soergel and Lunts in the case of flag varieties.
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2004
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-04-00230-4