Note on the Deodhar decomposition of a double Schubert cell

Details Note on the Deodhar decomposition of a double Schubert cell Note on the Deodhar decomposition of a double Schubert cell

2008-07-14

arxiv.org/abs/0807.2198v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

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 $3n-3$

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