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

8 pages

References in corpus (1)

• The T-equivariant Cohomology of Bott-Samelson varieties