On the variety of 1-dimensional representations of finite $W$-algebras in low rank

Jonathan Brown, Simon M. Goodwin

Let $\mathfrak{g}$ be a simple Lie algebra over $\mathbb{C}$ and let $e\in \mathfrak{g}$ be nilpotent. We consider the finite $W$-algebra $U(\mathfrak{g},e)$ associated to $e$ and the…