Note on the Deodhar decomposition of a double Schubert cell

Olivier Dudas (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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 $3n-3$

Mots clés: Schubert cells; Deodhar decomposition; Bialynicki-Birula decomposition

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]

Olivier Dudas. Note on the Deodhar decomposition of a double Schubert cell. 2008. ⟨hal-00296594⟩