Nearby cycles for parity sheaves on a divisor with simple normal crossings

The first author recently introduced a "nearby cycles formalism" in the framework of chain complexes of parity sheaves. In this paper, we compute this functor in two related settings: (i) affine space, stratified by the action of a torus, and (ii) the global Schubert variety associated to the first fundamental coweight of the group $PGL_n$. The latter is a parity-sheaf analogue of Gaitsgory's central sheaf construction.