论文标题
傅立叶变换为三角矩阵
Fourier transform as a triangular matrix
论文作者
论文摘要
令V为磁场上的有限维矢量空间，其两个元素具有给定的非排定形式。令[V]为V上的复杂值函数的矢量空间，让[V] _z为[V]的子组，由整数值函数组成。我们表明，存在[V] _z的Z-BASI，该_z由V的某些显式各向同性子空间的特征函数组成，使得从[V]到[V]相对于此基础的傅立叶转换的矩阵是三角形的。我们证明，这是一个结果的特殊情况，可为Weyl组中的任何双面细胞保留。
Let V be a finite dimensional vector space over the field with two elements with a given nondegenerate symplectic form. Let [V] be the vector space of complex valued functions on V and let [V]_Z be the subgroup of [V] consisting of integer valued functions. We show that there exists a Z-basis of [V]_Z consisting of characteristic functions of certain explicit isotropic subspaces of V such that the matrix of the Fourier transform from [V] to [V] with respect to this basis is triangular. We show that this is a special case of a result which holds for any two-sided cell in a Weyl group.
