Connected components in the intersection of two open opposite Schubert cells in real complete flag manifold

Details Connected components in the intersection of two open opposite Schubert cells in real complete flag manifold Connected components in the intersection of two open opposite Schubert cells in real complete flag manifold

1997-04-12

arxiv.org/abs/alg-geom/9704013v1

Mathematics

Algebraic Geometry

AMSTeX, 22 pages with 13 figures, available via http://www.math.kth.se/~mshapiro/

Scientific paper

In this paper we reduce the problem of counting the number of connected components in the intersection of two opposite open Schubert cells in the variety of real complete flags to a purely combinatorial question of counting the number of orbits of a certain intriguing group action in the space of upper triangular matrices with {0,1}-valued entries. The crucial step of our reduction uses the parametrization of the space of real unipotent totally positive upper triangular matrices introduced by Lusztig and Berenstein, Fomin, Zelevinski.

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