On decomposition of Bott-Samelson sheaves

We give an exact algorithm to calculate (under some GKM-restriction) the matrix describing the embedding B(s)x⊂B(s)x, where the first module is the costalk and the second one is the stalk at x of a Bott-Samelson module (sheaf) B(s). This allows us to calculate the first few terms of the decomposition of B(s) into a sum of indecomposable modules (sheaves) and to calculate the characters of Braden-MacPherson sheaves in some previously unknown cases.