2 problems

For every $K\in\{\mathbb{Q},\mathbb{R},\mathbb{C}\}$, every $n,d\ge 1$, and every symmetric tensor $T\in\operatorname{Sym}^d(K^n)$, the ordinary tensor rank equals the symmetric te…

Let $G$ be a subgroup of $\mathrm{SO}(3)$, let $\mathbb{T}$ be a tensor space with its $G$-representation, and let $\mathrm{C}\in\left[\mathbb{T}\otimes^S\mathbb{T}\right]^G$. Writ…