论文标题
反射组和正方形和锥
Reflection groups and cones of sums of squares
论文作者
论文摘要
我们认为真实形式的锥是正方形形式和（有限）反射组不变的总和。我们展示了这些组的表示理论如何允许使用这些锥体固有的对称性来提供更有效的描述。我们特别关注$ a_ {n} $，$ b_n $和$ d_n $ case，我们使用所谓的更高SpecHt多项式来对这些锥体进行统一的描述。这些描述使我们可以研究这些锥与非负形式的联系。特别是，我们给出了哈里斯（Harris）结果的新证明，哈里斯（Harris）表明，每个非负三元式甚至对称八粒形式都是正方形的总和。
We consider cones of real forms which are sums of squares forms and invariant by a (finite) reflection group. We show how the representation theory of these groups allows to use the symmetry inherent in these cones to give more efficient descriptions. We focus especially on the $A_{n}$, $B_n$, and $D_n$ case where we use so called higher Specht polynomials to give a uniform description of these cones. These descriptions allow us, for example, to study the connection of these cones to non-negative forms. In particular, we give a new proof of a result by Harris who showed that every non-negative ternary even symmetric octic form is a sum of squares.
