GEOMETRY OF FLAG MANIFOLDS
GEOMETRY OF FLAG MANIFOLDS
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DOI：
10.1142/s0219887806001399
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发表时间：
2006-09
影响因子：
1.8
通讯作者：
A. Arvanitoyeorgos
中科院分区：
文献类型：
--
作者：
A. Arvanitoyeorgos
A flag manifold is a homogeneous space M = G/K, where G is a compact semisimple Lie group, and K the centralizer of a torus in G. Equivalently, M can be identified with the adjoint orbit Ad(G)w of an element w in the Lie algebra of G. We present several aspects of flag manifolds, such as their classification in terms of painted Dynkin diagrams, T-roots and G-invariant metrics, and Kahler metrics. We give a Lie-theoretic expression of the Ricci tensor in M, hence reducing the Einstein equation on flag manifolds into an algebraic system of equations, which can be solved in several cases. A flag manifold is also a complex manifold, and this dual representation as a real and a complex manifold is related to a similar property of an infinite-dimensional manifold, the loop space, which in fact can be viewed as a "universal" flag manifold.
