2 problems

Let $V=\mathbb C[z_1,\dots,z_n]$ be filtered by polynomial degree, with $F_NV=\mathbb C[z_1,\dots,z_n]_{\le N}$. Let $W\in S^d\mathbb C^{n*}$ be a homogeneous polynomial of degree…

Let $H$ be the vector space underlying a sesquilinear form, and let $k$ be such that the associated dimension satisfies the exceptional case $\dim H=2k$. The relevant transformatio…