Stable-range conjecture for twisted cohomology of $\operatorname{SL}(n,\mathbb{Q})$

Let $\ul\la$ be a bipartition and let $n\ge l(\ul\la)$ be an integer. For $i=1,\dots,n$, define

$$a(i)=\frac{n+1}{2}-i-\alpha+\mu_i,$$

where $\mu_i$ is given in the source, and let $C'(\operatorname{SL}(n,\mathbb{Q}),V_{\ul\la})$ denote the stable-range invariant under consideration. Stable-range conjecture. One has

$$C'(\operatorname{SL}(n,\mathbb{Q}),V_{\ul\la})=\min\{i\in\{1,\dots,n\}\mid a(i)\le 0\text{ or }a(n+1-i)\ge 0\}-2.$$

The conjecture is motivated by computations and would completely determine $C'(\operatorname{SL}(n,\mathbb{Q}),V_{\ul\la})$, including the range $n< B(\ul\lambda)$ where the preceding theorem gives no information. Its resolution status is not specified in the supplied text.