2 problems

Let $\mathfrak{sp}_{2n}$ be the symplectic Lie algebra, let $V_{\nu}$ be its standard representation, let $V_{\mathbf{0}}$ be its trivial representation, and let $V_{\lambda}$ be t…

Let $X$ be a Dynkin diagram of finite type, let $I=I(X)$ be its set of nodes, and let $A=(a_{ij})$ be the associated Cartan matrix. The electrical Lie algebra $\mathfrak{e}_{X}$ is…