I'm trying to understand the link between subset of the simple roots and parabolic subgroups in the case of $\text{GL}_n$. More precisely, let $\Delta= \{\alpha_{i,i+1}\}$ be the usual set of simple roots for $\text{GL}_n$ and let $I \subset \Delta$ be a subset. What is the parabolic subgroup of $\text{GL_n}$ associated to $I$ ?
I would be very interested in a reference where this is worked out in detail (along with the theory).