2015/01/22 by Eichinger, B. E.
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1504.01618
Flag manifolds are shown to describe the relations between configurations of distinguished points (topologically equivalent to punctures) embedded in a general spacetime manifold. Grassmannians are flag manifolds with just two subsets of points selected out from a set of N points. The geometry of Grassmannians is determined by a group acting by linear fractional transformations, and the associated Lie algebra induces transitions between subspaces. Curvature tensors are derived for a general flag manifold, showing that interactions between a subset of k points and the remaining N-k points in the configuration is determined by the coordinates in the flag manifold.