11 problems

Let $Q_m$ be the quasi-invariant polynomial space for $n=3$, and let the ring of symmetric polynomials act on it by multiplication. Three-variable freeness conjecture. The space…

Kashiwara-type equivalence conjecture. The direct image functor $i_+$ is an equivalence of categories, with quasi-inverse

Let ${\cal R}$ be a Coxeter system, let $G$ be its associated Coxeter group, let $S^G$ denote the ring of invariant polynomials, and let $Q^{\cal R}$ denote the ring of quasi-invar…

Let $Q^{{{\cal A}_n(m)}}$ be the algebra of quasi-invariants for the deformed configuration ${{\cal A}_n(m)}$, and let $P^{{{\cal A}_n(m)}}$ be its algebra of invariants. For suffi…

Let ${{\cal A}_n(m)}$ and ${{\cal C}_{n+1}(m,l)}$ be the deformed configurations with multiplicities $m$ and $(m,l)$, respectively, and let $P_{stable}^{{{\cal A}_n(m)}}$ and…

Ren–Xu's conjecture. If the Hilbert series of $Q_m(n,\mathbf{F}_p)$ differs from that of $Q_m(n,\mathbf{Q})$, then there exist integers $a\geq 0$ and $k\geq 0$ satisfying the displ…

Let $m$ and $n$ be positive integers, let $q$ be a nonzero complex number, and let $Q_{m,q}(n)$ and $Q_m(n,\mathbb{C})$ denote the $q$-deformed and ordinary $m$-quasi-invariant pol…

Let $Q_{m,q}(3)$ denote the algebra of $q$-deformed $m$-quasi-invariant polynomials in three variables, and let $m$ be a nonnegative integer. Hilbert-series conjecture. Based on ca…

Let $Q_m$ be a space of twisted quasi-invariant polynomials and let its $q$-deformation be the corresponding deformation studied for the twisted quasi-invariant construction. Gener…

Let $m$ be a nonnegative integer, let $f_1,f_2,\dots,f_n$ be one-variable meromorphic functions, and let $Q_m(f_1,\dots,f_n)$ be the space of polynomials…

Let $Q_m(n)$ denote the space of quasi-invariant polynomials in $n$ variables with parameter $m$, and let $p$ be prime. Suppose the Hilbert series of $Q_m(n)$ over $\mathbb F_p$ di…