7 problems

Let $W$ be a real reflection group with reflection representation $V$. A positive integer $r$ is $W$-good if, for every parameter $c$ with $|c|=r$, the Cherednik algebra $H_c(W)$ a…

Finite-dimensional representation conjecture. The algebra ${\mathsf{H}}_c$ has a nonzero finite-dimensional representation $V$ if and only if $r$ is coprime to $n$; moreover, in th…

Let ${\mathscr{B}_{\bm s,\bm \varepsilon}}$ be the twisted super Yangian of type AIII, let $V(\bm\mu(u))$ be an irreducible ${\mathscr{B}_{\bm s,\bm \varepsilon}}$-module, and let…

Let $\mathfrak g$ be a semisimple simply-laced Lie algebra, let $\lambda$ and $\mu$ be dominant coweights, let $Y^\lambda_\mu(\mathbf R)$ be the corresponding truncated shifted Yan…

Let $G=W(H_4)$ and let $L_{(c,c)}(\phi_{9,2})$ denote the irreducible module for the rational Cherednik algebra with equal parameters $(c,c)$, labelled by the representation…

Let $G=W(H_4)$, let $c$ be the Cherednik parameter, and let $L_c(\phi_{25,4})$ denote the irreducible module labelled by the representation $\phi_{25,4}$ of $G$. Norton's conjectur…

Let $G=W(H_4)$, let $c$ be the Cherednik parameter, and let $L_c(\rho)$ denote the irreducible module labelled by the representation $\rho$ of $G$. Let $\rho=\phi_{9,2}$ and let…