We study the properties of B-branes in a class of nonabelian GLSMs realizing the canonical line bundle \(K_{Gr(2,N)}\) in their geometric phase. By analysing the hemisphere partition function, i.e. B-brane central charge, we propose a grade restriction rule and the corresponding window categories for a specific class of paths between phases. We find very striking differences between the cases of N even and N odd. In particular, for the case of N even, we suggest that more than one window category can be possible, for a fixed path. A detailed computation of the open Witten index and some monodromies provides evidence for our proposal for window categories. In addition, we make some remarks about B-branes on the strongly coupled phase, for the case \(N=4\) , based on our window proposal.
