15 problems

Suppose $c_0=j/k$ with $k$ and $j$ relatively prime positive integers, and $2\leq k\leq n$. Let $\mathbf{C}[\mathfrak{h}]$ be the polynomial representation, and let…

Let $Z_{p,m}$ and $Z_{p,m}'$ be the submodules defined above, and let $E_1$ be the first member of the corresponding filtration of submodules. EZ submodule conjecture. With the not…

Let $H_{1/e}(\mathfrak{S}_n)$ be the Cherednik algebra of the symmetric group, and let $L(\lambda)$ be a unitary simple module labeled by a partition $\lambda$ of $n$. Berkesch–Gri…

Let $e\mathfrak{L}_{1/p+k,\epsilon=1}(\operatorname{triv})$ be the graded vector space considered in the source, let $\mathfrak{m}$ be its indicated filtration ideal, and let $Z_p$…

The paper studies odd Dunkl and odd Cherednik operators, including their relation to noncommutative symmetric-function structures. Geometric-connection conjecture. The authors conj…

Let $\mathcal A_\hbar$ denote the quantized Coulomb-branch algebra in the adjoint case, and let the spherical part of the graded Cherednik algebra be the corresponding spherical Ch…

Let $B_0$ be the principal block, let $\Lambda_\lambda$ and $\bar{\Gamma}_\lambda$ be the poset and graph subsets defined by the algorithm, and let $d(\mu,\lambda)$ be the grading…

Let $W=B_{2n}=G(2,1,2n)$ and let the parameter $c=1/(2n)$ be constant. Write $\Delta_i$ and $\Delta_{2n-i}$ for the standard-module sums specified in the preceding theorem, and let…

The paper considers quiver Temperley–Lieb algebras of type $G(l,1,n)$ arising as saturated quotients of Webster's algebra for a FLOTW weighting, with standard modules indexed by on…

Rouquier's conjecture. Every coset $c+\mathfrak{p}_{\mathbb{Z}}$ contains a parameter $c$ such that

A Cherednik parameter $c$ is called totally aspherical if, for every parabolic subgroup $W'\subseteq W$, the spherical Cherednik algebra $e_{W'}H_c(W')e_{W'}$ has no nonzero finite…

Recursive-extension conjecture. One can choose $F_2$ without adding $p$-th powers and continue the recursion to construct $F_3,F_4,\ldots$ indefinitely.

Gorenstein and palindromicity conjecture. If $\tau$ is trivial, then $M_c(S_n,\mathfrak{h},\tau)/J_c(S_n,\mathfrak{h},\tau)$ is Gorenstein for all $n$, both when $c\in\mathbf{F}_p$…

Degree-sum conjecture. The sum of the degrees in a minimal generating set of $J_{c+1}(S_n,\mathfrak{h},\tau)$ is exactly $n!$ greater than the corresponding sum for…

Let $G$ be a finite group acting on a vector space $\mathfrak{h}$, let $\mathfrak{h}^*$ be its dual, and let $b\in\mathfrak{h}$ and $\lambda\in\mathfrak{h}^*$. Write $G_b$ and…