Graded Lie algebras and intersection cohomology

Details Graded Lie algebras and intersection cohomology Graded Lie algebras and intersection cohomology

2006-04-25

arxiv.org/abs/math/0604535v2

Mathematics

Representation Theory

33 pages

Scientific paper

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.

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