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arXiv 0910.41472009-10math.RT

反轨道配合物的研究

Study of antiorbital complexes

G. Lusztig

备注：: 32 pages

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摘要：

设E是有限域的代数闭包上的有限维向量空间，其线性作用是连通线性代数群K的线性作用，E'是对偶空间. E上的l-adic层复形称为轨道复形，如果它是一个支撑是单个K-轨道的简单反常层。E上的l-adic层复形称为双轨复形，如果它是轨道的，并且如果它的Deligne傅里叶变换是E '上的轨道。在本文中，我们研究的情况下，E是一个约化李代数的半单自同构的特征空间的双轨道复合物的例子。

英文摘要：

Let E be a finite dimensional vector space over an algebraic closure of a finite field with a given linear action of a connected linear algebraic group K and let E' be the dual space. A complex of l-adic sheaves on E is said to be orbital if it is a simple perverse sheaf whose support is a single K-orbit. A complex of l-adic sheaves on E is said to be biorbital if it is orbital and if its Deligne Fourier transform is orbital on E'. In this paper we study examples of biorbital complexes arising in the case where E is an eigenspace of a semisimple automorphism of a reductive Lie algebra.

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