论文标题
作用于紧凑型Tori的Weyl组的轨道空间：统一和显式多项式描述
Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description
论文作者
论文摘要
晶体根系的Weyl群对紧凑的圆环具有非线性作用。此动作的轨道空间是紧凑的基本半代数集。我们为A，B，C，D和G的Weyl组提供了此组的多项式描述。我们的描述是通过多项式矩阵不等式给出的。新颖性在于通过Hermite二次形式的方法和矩阵条目的封闭公式。 非线性Weyl组作用的轨道空间是广义Chebyshev多项式的正交区域。在此多项式的基础上，我们表明，获得的五种类型的矩阵遵循相同的，令人惊讶的简单模式。这适用于用晶体学对称的三角多项式的优化。
The Weyl group of a crystallographic root system has a nonlinear action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a polynomial description of this set for the Weyl groups of type A, B, C, D and G. Our description is given through a polynomial matrix inequality. The novelty lies in an approach via Hermite quadratic forms and a closed formula for the matrix entries. The orbit space of the nonlinear Weyl group action is the orthogonality region of generalized Chebyshev polynomials. In this polynomial basis, we show that the matrices obtained for the five types follow the same, surprisingly simple pattern. This is applied to the optimization of trigonometric polynomials with crystallographic symmetries.
