论文标题
$ Q $ - 横时多项式和群体不变的傅立叶变换在有限的字段上
$q$-Hypergeometric polynomials and group-invariant Fourier transformations over a finite field
论文作者
论文摘要
通过傅立叶变换，对有限阿贝尔组的任何组不变函数都会转变为角色组上的群体不变函数。在本文中，我们计算在特定碱基下此转换的矩阵元素。更具体地说，我们在有限的字段和线性动作上处理一些向量空间。然后，在足够的碱基下的矩阵元素由krawtchouk或offine q-krawtchouk多项式表示。为了计算，我们构建了一个交换图，该图结合了组不变傅立叶变换的两个设置。我们将其应用于每个示例的不同尺寸转换，并将其归纳求解。我们指出的是矩阵元素与有限的gelfand对的区域球形函数有关。
By the Fourier transformations, any group-invariant functions over finite Abelian groups are transformed into group-invariant functions over the character groups. In this paper, we calculate matrix elements of this transformations under specific bases. More specifically, we deal with some vector spaces over a finite field and linear actions. Then the matrix elements under adequate bases are expressed by Krawtchouk or Affine q-Krawtchouk polynomials. For calculations, we construct a commutative diagram which combines two settings of group-invariant Fourier transformations. We apply it to different sized transformations of each example, and solve it inductively. We remark the matrix elements are related to the zonal spherical functions of finite Gelfand pairs.
