2 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 $\mathscr{R}_{\alpha}^{\Lambda}$ be the cyclotomic quiver Hecke algebra over a ground field $K$, let $d_{\Lambda,\alpha}$ denote the r…