E轨道函数
E-Orbit Functions
摘要：
我们回顾并进一步发展了$E$ -轨道函数理论。它们是欧几里得空间$E_n$上的函数，由多元指数函数通过Weyl群$W$的偶数部分$W_{e}$对称化而得到，对应于Coxeter-Dynkin图。描述了这些函数的性质。它们与由指数函数通过Weyl群$W$对称化和反对称化得到的对称和反对称轨道函数密切相关。由积分参数确定的$E$ -轨道函数对于对应于$W$的仿射Weyl群的偶数部分$W^{\rm aff}_{e}$是不变的. $E$轨道函数确定对称傅立叶变换，其中这些函数用作变换的核。他们还确定了一个变换的一组$W^{\rm aff}_{e}$（离散$E$ -轨道函数变换）的基本域$F^{e}$的一组有限的点。
英文摘要：
We review and further develop the theory of $E$-orbit functions. They are functions on the Euclidean space $E_n$ obtained from the multivariate exponential function by symmetrization by means of an even part $W_{e}$ of a Weyl group $W$, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. They are closely related to symmetric and antisymmetric orbit functions which are received from exponential functions by symmetrization and antisymmetrization procedure by means of a Weyl group $W$. The $E$-orbit functions, determined by integral parameters, are invariant with respect to even part $W^{\rm aff}_{e}$ of the affine Weyl group corresponding to $W$. The $E$-orbit functions determine a symmetrized Fourier transform, where these functions serve as a kernel of the transform. They also determine a transform on a finite set of points of the fundamental domain $F^{e}$ of the group $W^{\rm aff}_{e}$ (the discrete $E$-orbit function transform).
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