2 problems

Let $k,N$ be positive integers and set $n=\lfloor N/2\rfloor$. For $1\leq a,b\leq N-1$, let $C_{ab}$ be the Cartan integers of $\operatorname{A}_{N-1}$, and define…

For $1\leq a,b\leq N-1$, let $C_{ab}$ be the Cartan integers of the Lie algebra $\operatorname{A}_{N-1}$, with $C_{aa}=2$, $C_{a,a\pm1}=-1$, and $C_{ab}=0$ otherwise. For…