Note on the Deodhar decomposition of a double Schubert cell
Abstract
We show that for an algebraic reductive group G, the partition of a double Schubert cell in the flag variety G/B defined by Deodhar, and coming from a Bialynicki-Birula decomposition, is not a stratification in general. We give a counterexample for a group of type Bn, where the closure of some specific cell of dimension 2n has a non-trivial intersection with a cell of dimension 3n-3
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