The space of invariant functions on a finite Lie algebra
The space of invariant functions on a finite Lie algebra
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有限李代数上的不变函数空间
DOI：
10.1090/s0002-9947-96-01492-4
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发表时间：
1996
影响因子：
1.3
通讯作者：
G. Lehrer
中科院分区：
文献类型：
--
作者：
G. Lehrer
证明了有限李代数上伴随不变函数空间上的傅里叶变换和对偶运算是可交换的。这一结果是适用于给公式的傅里叶变换的“布劳尔函数”-即一个其值在X只取决于半单部分Xs的X和对偶的卷积的任何功能与斯坦伯格功能。几何上的应用包括Weyl群的Springer表示的性质的评价和G/T上局部系统的等变上同调的研究，其中T是基础约化群G的极大环面.
We show that the operations of Fourier transform and duality on the space of adjoint-invariant functions on a finite Lie algebra commute with each other. This result is applied to give formulae for the Fourier transform of a “Brauer function”—i.e. one whose value at X depends only on the semisimple part Xs of X and for the dual of the convolution of any function with the Steinberg function. Geometric applications include the evaluation of the characters of the Springer representations of Weyl groups and the study of the equivariant cohomology of local systems on G/T , where T is a maximal torus of the underlying reductive group G.