Conformal and fractional boundary states in the symmetric orbifold of the level one SU (2) WZW model

We study the space of the allowed boundary states in a particular c = 1 conformal field theory, the symmetric orbifold of the level one SU(2) WZW model, where the orbifolding group G is a generic binary finite subgroup of SU(2). We especially construct generic boundary states in the orbifold, which can be extended from the Cardy states decomposed into Virasoro Ishibashi states. Our result involves conformal boundary states parameterized by the quotient SU(2)/G, and the fractional boundary states sitting at every fixed-point in the quotient. We find also that a conformal boundary state at a fixed-point in the quotient becomes a linear combination of the fractional boundary states sitting at the fixed-point. To be complete, we check the mutual consistency among all the boundary states we construct.