Graded Lie algebras and intersection cohomology
Abstract
Description
Let i be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G^i be the centralizer of the image i. Let LG be the Lie algebra of G and let L_nG (n integer) be the summands in the direct sum decomposition of LG determined by i. Assume that n is not zero. For any G^i-orbit O in L_nG and any irreducible G^i-equivariant local system L on O we consider the restriction of some cohomology sheaf of the intersection cohomology complex of the closure of O with coefficients in L to another orbit O' contained in the closure of O. For any irreducible G^i-equivariant local system L' on O' we would like to compute the multiplicity of L' in that restriction. We present an algorithm which helps in computing that multiplicity.
33 pages
33 pages