for $p+q\leq k+1$. For $2\leq p\leq n-1$ the Levi subgroups, having disconnected diagrams, usually split as direct or semidirect products of two groups whose types belong to the connected components of the Coxeter diagrams.

(Qp) at (-1,1.6) [$Q_p$]{}; (K) at (-1,0.8) [$K_p$]{}; (Kp) at (-1,0) [$K'_p$]{}; in [0,1,2,3,4]{} [ (,1.6) circle (.7mm);]{} (1,1.6) – (2,1.6); (2,1.6) – (3,1.6); (3,1.6) – (4,1.6); (0,1.6 + .05) – (1,1.6 + .05); (0,1.6 - .05) – (1,1.6 -.05); in [0,.8]{} [ in [6,7,8,9]{} [ (,) circle (.7mm);]{} (6,) – (7,); (7,) – (8,); (8,) – (9,); ]{} (9,.8) – (10,.8); (10,.8) circle (.7mm); (0) at (0,-.6) [$1$]{}; (1) at (1,-.6) [$2$]{}; (3) at (4,-.6) [$p-1$]{}; (4) at (5,-.63) [$p$]{}; (5) at (6,-.6) [$p+1$]{}; (7) at (9,-.62) [$n$]{}; (8) at (10,-.6) [$n+1$]{};

This means that there are groups $Q_p$, $K_p$ and $K'_p$ of types $\{i_1,\ldots,i_{p-1}\}$, $\{i_{p+1},\ldots,i_{n+1}\}$ and $\{i_{p+1},\ldots,i_n\}$, respectively, such that $L_p=Q_p\ltimes K_p$ and $L'_p=Q_p\ltimes K'_p$. The modules $M_p$ are constructed in such a fashion that the groups $K_p$ and $K'_p$ act trivially on $M_p$. If we know that relative *integral* homology of the subgroups $K_p$ and $K'_p$ vanishes, we can produce zeroes in the first page $E^1_{p,q}$ by using a relative Lyndon/Hochschild-Serre spectral sequence.

