Dennis–Vaserstein type decompositions

We prove a generalisation of Dennis–Vaserstein decomposition for an arbitrary pair of maximal parabolic subgroups $P_r$ and $P_s$ in the general linear group $\mathrm{GL}(n,R)$, provided that $r-s\geq\mathrm{sr}(R)$. The usual Dennis–Vaserstein decomposition is the special case where $r=n-1$, $s=1$. Bibl. – 23 titles.