A Classification of Multiplicity Free Actions
A Classification of Multiplicity Free Actions
复制标题
多重自由动作的分类
DOI：
10.1006/jabr.1996.0113
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发表时间：
1996
影响因子：
0.9
通讯作者：
G. Ratcliff
中科院分区：
文献类型：
--
作者：
C. Benson;G. Ratcliff
复代数群G在仿射簇V上的作用称为多重自由，如果G的每个不可约表示在V上的正则函数环C [V]中至多出现一次。本文讨论了向量空间V和G在V上线性作用的经典情形. V.Kac对不可约线性重数自由作用进行了分类。这里的重点是非不可约线性多重自由作用。我们展示了许多不分解为不可约作用的直积的这样的作用。我们的主要结果提供了一个分类的所有线性重自由行动的向量空间。
Abstract The action of a complex algebraic groupGon an affine varietyVis said to be multiplicity free if each irreducible representation ofGoccurs at most once in the ring C [V] of regular functions onV. This paper concerns the classical setting whereVis a vector space andGacts linearly onV. The irreducible linear multiplicity free actions have been classified by V. Kac. The focus here is on nonirreducible linear multiplicity free actions. We exhibit many such actions which do not decompose as direct products of irreducible actions. Our main results provide a classification for all linear multiplicity free actions on a vector space.