Twisted D-branes of the WZW model and level-rank duality

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