9 problems

Let $H_1,H_2,\ldots,H_n$ be the algebraically independent generators of the algebra of invariant differential operators on Siegel upper half-space, and let $q_j$ denote the corresp…

Let $(\mathfrak{g},\sigma)$ be a symmetric pair, with Cartan decomposition $\mathfrak{g}=\mathfrak{k}\oplus\mathfrak{p}$. Let $U(\mathfrak{g})$ be the universal enveloping algebra,…

Gamma annihilator conjecture. Then

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…

The Grozman operator is an indecomposable invariant differential operator of order $3$ in the exceptional case $m=1$. The Lie algebra of vector fields on the line satisfies … where…

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…

Let $\mathbb H_n$ be the Siegel upper half-space, let $H_j=\operatorname{tr}(A^{(j)})$ for $j=1,2,\ldots,n$, where the matrices $A^{(j)}$ are defined recursively from the invariant…

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…