Stability inequalities and universal Schubert calculus of rank 2

@article{Berenstein2010StabilityIA,
  title={Stability inequalities and universal Schubert calculus of rank 2},
  author={Arkady Berenstein and Michael Kapovich},
  journal={Transformation Groups},
  year={2010},
  volume={16},
  pages={955-1007}
}
The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each “sufficiently rich” spherical building Y of type W we associate a certain cohomology theory $ H_{BK}^*(Y) $ and verify that, first, it depends only on W (i.e., all such buildings are “homotopy equivalent”), and second, $ H_{BK}^*(Y) $ is the associated graded of the coinvariant algebra of W under certain filtration. We also construct the dual homology “pre-ring” on Y. The… 
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