On decomposition of Bott-Samelson sheaves

2012/01/06 by Shchigolev, Vladimir
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1201.1396

Abstract

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.

Related

• Bases of T-equivariant cohomology of Bott-Samelson varieties
• Decomposition of Perverse Sheaves on Plane Line Arrangements
• Braden-MacPherson sheaves on alcoves
• Bott-Samelson Varieties and Configuration Spaces
• Algebraic representations and constructible sheaves