منابع مشابه
Quantum Cohomology of Flag Manifolds
In this paper, we study the (small) quantum cohomology ring of the partial flag manifold. We give proofs of the presentation of the ring and of the quantum Giambelli formula for Schubert varieties. These are known results, but our proofs are more natural and direct than the previous ones. One of our goals is to give evidence of a relationship between universal Schubert polynomials, which give t...
متن کاملRiemannian Symmetries in Flag Manifolds
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z2 -symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. The conditions for a metric adapted to the Z2-symmetric structure to be naturally reductive are detailed for the flag manifold SO(5)/SO(2)× SO(2)× SO(1).
متن کاملFlag Manifolds and Toric Geometry
1.1. Flag Manifolds. One of the best understood examples of algebraic varieties is the flag manifold. One is first interested in flag varieties as they are well-defined examples for many basic concepts. Besides this, however, one can find that they deserve individual attention, for they naturally arise in many circumstances, e.g. in the theory of characteristic classes of vector bundles, mirror...
متن کاملLevi-civita Connections of Flag Manifolds
For any flag manifold G/T we obtain an explicit expression of its Levi-Civita connection with respect to any invariant Riemannian metric.
متن کاملAdmissible Representations and Geometry of Flag Manifolds
We describe geometric realizations for various classes of admissible representations of reductive Lie groups. The representations occur on partially holomorphic cohomology spaces corresponding to partially holomorphic homogeneous vector bundles over real group orbits in complex flag manifolds. The representations in question include standard tempered and limits of standard tempered representati...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0424840-4