5 problems

Gamma spherical Harish-Chandra conjecture. There is a filtration-preserving algebra isomorphism

Let ${\mathscr P}_{n,m}$ be the Siegel–Jacobi space, and let $D_j$ for $1\leq j\leq n$ and $\Omega_{pq}^{(k)}$ for $0\leq k\leq n-1$ and $1\leq p\leq q\leq m$ be the invariant diff…

Let ${\mathscr P}_{n,m}$ be the Siegel–Jacobi space. Let $D_j$ for $1\leq j\leq n$ and $\Omega_{pq}^{(k)}$ for $0\leq k\leq n-1$ and $1\leq p\leq q\leq m$ be the invariant differen…

Let $X=G/K$ be a simple Hermitian symmetric space, where $K$ is a compact subgroup of $G$. For each $m\in\mathbb{N}$, let $L_m$ denote the higher Laplacian of order $2m$ on $X$, wi…

The equivariant quantization conjecture. The quantization has the following properties: (1) it does not exist or is not unique if and only if, for some $1\leq l\leq k$, there is a…