3 problems

Let $(W,S)$ be a Coxeter system, let $R$ be the coefficient ring, and let $\mathcal{H}$ be its Hecke algebra. The cocenter is the quotient $\mathcal{H}/[\mathcal{H},\mathcal{H}]$,…

Let $\Lambda\in P^+$ and $\alpha\in Q^+$. Let $\PD$ be the set of piecewise dominant sequences with respect to $\Lambda$, and define an equivalence relation by $\mu\sim\nu$ if and…

Let $\Lambda\in P^+$ and $\alpha\in Q^+$. Let $\mathscr{R}_{\alpha}^{\Lambda}$ be the cyclotomic quiver Hecke algebra over a ground field $K$, let $d_{\Lambda,\alpha}$ denote the r…