Integrality conjecture for functional dimensions

Let $G$ be a connected unipotent algebraic group, let $e$ be a minimal idempotent of ${\mathscr D}_G(G)$, and let its functional dimension be $d_e=(\dim G-n_e)/2$. The integrality conjecture. If the ${\mathbb L}$-packet corresponding to $e$ is trivial, then $d_e$ is an integer.