10 problems

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

Null-vector characterization conjecture. Each ideal of $H_{1,\eta}(A_{n-1})$ is the set of null-vectors of the degenerate bilinear form $B_{sp}$ for some $\varkappa$-trace $sp$ on…

Etingof's refined representation-count conjecture. The number of isomorphism classes of finite-dimensional irreducible representations of $H_{c,k}(\Gamma_n)$ is

Etingof's refined filtration conjecture. For either filtration, there exists an isomorphism of vector spaces

Etingof's representation-count conjecture. The number of isomorphism classes of finite-dimensional irreducible representations of $H_{c,k}(\Gamma_n)$ is

Etingof's irrational-parameter filtration conjecture. For either filtration, there exists an isomorphism of vector spaces

Etingof's aspherical-locus conjecture. The aspherical locus is the union of the hyperplanes $E_{m,N}$ for $1\le N\le m-1$ and the hyperplanes $H_{\alpha,m,N}$ satisfying the stated…

Etingof's simplicity conjecture. The algebra $H_{c,k}(\Gamma_n)$ is simple if and only if $(\lambda,k)$ belongs to none of the hyperplanes $E_{m,N}$ or $H_{\alpha,m,N}$.

Etingof's q-nondegeneracy conjecture. If $q$ is not a root of unity, then the form $(,)_q$ is nondegenerate.

Etingof's positivity conjecture. The inner product $(,)$ is symmetric and positive definite, and in particular nondegenerate.