Abstract (eng)
The main topic addressed in this work is the geometry of D-branes in the WZW model on a compact, simple, simply connected Lie group. At first, we recall some main ideas related to open strings in group manifolds and their gluing conditions. The D-branes given in terms of some special gluing conditions correspond to twisted conjugacy classes with respect to an automorphism of the Lie group. After setting up some mathematical machinery to allow us to work with them, we parametrize the space of twisted conjugacy classes using a rather explicit computation and comparing it with the abstract method. We also point out some(what we believe to be) errors in a previous work on this topic on which both of the methods we use agree. Finally, as stabilizer of the twisted conjugacy classes also fi t into the picture of D-branes, we compute them explicitly and again more abstractly for SU(4).