2 problems

Assume that $\mathfrak{g}$ is of affine type, with simple-root index set $I$, distinguished vertex $0\in I$, and $I_{0}:=I\setminus\{0\}$. For $i\in I_{0}$, let $\varpi_i$ be a fun…

Lusztig's almost orthogonality conjecture. The global base $\{G(b)\mid b\in\mathcal B(\lambda)\}$ of $V(\lambda)$ satisfies the almost orthogonality property with respect to the ge…