论文标题
对称调整的革兰氏谱图
Symmetry Adapted Gram Spectrahedra
论文作者
论文摘要
本文探讨了光谱锥的几何结构，称为对称性的PSD锥体，以及对称性多项式的对称化适用的革兰氏谱。特别是，我们确定了对称性调整的PSD锥的维度，描述其极端射线，并讨论其矩阵表示的结构。我们还考虑了对称对称多项式特定家族的对称性适应的革兰氏光谱，包括二进制对称多项式，四边形和三元四分之一的四分之一和六序，这使我们对这些对称的SOS多项式物质有了进一步的了解。最后，我们讨论了由对称函数不平等产生的正方形和对称多项式总和的应用。
This paper explores the geometric structure of the spectrahedral cone, called the symmetry adapted PSD cone, and the symmetry adapted Gram spectrahedron of a symmetric polynomial. In particular, we determine the dimension of the symmetry adapted PSD cone, describe its extreme rays, and discuss the structure of its matrix representations. We also consider the symmetry adapted Gram spectrahedra for specific families of symmetric polynomials including binary symmetric polynomials, quadratics, and ternary quartics and sextics which give us further insight into these symmetric SOS polynomials. Finally, we discuss applications of the theory of sums of squares and symmetric polynomials which arise from symmetric function inequalities.
