Minimal nilpotent finite $W$-algebra and cuspidal module category of ${\mathfrak{sp}}_{2n}$

Genqiang Liu, Mingjie Li

Let $U_S$ be the localization of $U({\mathfrak{sp}}_{2n})$ with respect to the Ore subset $S$ generated by the root vectors $X_{{\epsilon }_1-{\epsilon }_2},\dots ,X_{{\epsilon }_1-{\epsilon }_n},X_{2{\epsilon }_1}$. We show that th…