Note on the Deodhar decomposition of a double Schubert cell

Understand

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 B$_n$, where the closure of some specific cell of dimension $2n$ has a non-trivial intersection with a cell of dimension $3n-3$