Twisted D-branes of the suˆ(N)K WZW model and level-rank duality

We analyze the level-rank duality of ωc-twisted D-branes of suˆ(N)K (when N and K>2). When N or K is even, the duality map involves Z2-cominimal equivalence classes of twisted D-branes. We prove the duality of the spectrum of an open string stretched between ωc-twisted D-branes, and ascertain the relation between the charges of level-rank-dual ωc-twisted D-branes.