Graded Lie Algebras and Intersection Cohomology
Graded Lie Algebras and Intersection Cohomology
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分级李代数和交交上同调
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发表时间：
2006
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通讯作者：
G. Lusztig
中科院分区：
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作者：
G. Lusztig
设i是C上乘法群到连通约化代数群的同态。设G i为图像i的中心化子。设LG是G的李代数，LnG（n个整数）是LG的直和分解中由i确定的和项.假设n不为零。对于Ln G中的任意G ι-轨道（mathcal{O}）和（mathcal{O}）上的任意不可约G ι-等变局部系（mathcal{L}），考虑了（mathcal {O}）的闭包的交上同调复形的上同调层与（mathcal{L}）中的系数的限制.对于（mathcal{O}^prime）上的任何不可约G i-等变局部系统（mathcal{L}^prime），我们希望计算（mathcal{L}^prime）在该限制下的重数。我们提出了一个算法，这有助于计算的多重性。
Let ι be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G ι be the centralizer of the image ι. Let LG be the Lie algebra of G and let L n G (n integer) be the summands in the direct sum decomposition of LG determined by ι. Assume that n is not zero. For any G ι-orbit (mathcal{O}) in L n G and any irreducible G ι-equivariant local system (mathcal{L}) on (mathcal{O}) we consider the restriction of some cohomology sheaf of the intersection cohomology complex of the closure of (mathcal{O}) with coefficients in (mathcal{L}) to another orbit (mathcal{O}^prime) contained in the closure of (mathcal{O}). For any irreducible G ι-equivariant local system (mathcal{L}^prime) on (mathcal{O}^prime) we would like to compute the multiplicity of (mathcal{L}^prime) in that restriction. We present an algorithm which helps in computing that multiplicity.