4 problems

Let $m,n$ be coprime positive integers. Let $\mathcal{H}_{(m,n)}(X;q,t)$ be the Hikita polynomial, let $\Lambda$ be the ring of symmetric functions in $X$, and let…

Let $m,n$ be coprime positive integers, let $H_{n,c}$ be the rational Cherednik algebra of type $A$ with $c=m/n$, and let $L_{m/n}$ be its unique finite-dimensional representation.…

Residue-class unimodality conjecture. For every residue class $r$, $0\leq r<a$, the coefficients of $q^{ak+r}$ in $\mathbf{Cat}_{a,b}(q)$ are unimodal. The conjecture refines ordin…

Coset age conjecture. There is an age function $\iota$ on the cosets $\mathfrak{c}\in\boldsymbol{\Lambda}/\boldsymbol{\Lambda}_T$ such that