2 problems

Let $k,n$ be positive integers, set $N=2n+1$ and $p=1$, and let $C_{ab}$ be the Cartan matrix of type $\textup{A}_{N-1}$. For nonnegative integers $m_i^{(a)}$, define the associate…

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…