Harmonic polynomials and peak sets of reflection groups
Harmonic polynomials and peak sets of reflection groups
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谐波多项式和反射群的峰值集
DOI：
10.1007/bf00147428
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发表时间：
1989
影响因子：
0.5
通讯作者：
C. Dunkl
中科院分区：
文献类型：
--
作者：
C. Dunkl
在欧几里得空间中固定原点的有限反射群作用于单位球面上的任何点，而不是任何反射超平面上的任何点，以生成正则轨道。多项式函数对这样的轨道的限制空间同构于群代数。Delsarte [4]研究了某些（约翰逊）结合方案上的所谓离散调和，这些结合方案也是有限齐性空间。当轨道为“峰值集”时，正则轨道上的函数空间可被赋予“球调和”结构（这意味着存在类似于O/~ x~和A的算子交换集，以及相关的正交结构）。这里我们指的是单位球面上的点的集合，其中函数
A finite reflection group fixing the origin in Euclidean space acts on any point on the unit sphere, and not in any of the reflecting hyperplanes, to generate a regular orbit. The space of restrictions of the polynomial functions to such an orbit is isomorphic to the group algebra. Delsarte [4] studied so-called discrete harmonics on certain (Johnson) association schemes, which are also finite homogeneous spaces. In these cases, however, the stabilizer group of a point is nontrivial.The space of functions on a regular orbit can be given a'spherical harmonic'structure (this implies the existence of a commutative set of operators analogous to O/~ x~ and A, and an associated orthogonality structure), when the orbit is a'peak set'. By this we mean the set of points on the unit sphere where the function