The conformal boundary states for SU(2) at level 1

For the case of the SU(2) WZW model at level one, the boundary states that only preserve the conformal symmetry are analysed. Under the assumption that the usual Cardy boundary states as well as their marginal deformations are consistent, the most general conformal boundary states are determined. They are found to be parametrised by group elements in SL(2,C).