The null identities for boundary operators in the $(2,2p+1)$ minimal gravity

By using the matrix-model representation, we show that correlation numbers of boundary changing operators (BCO) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCO in terms of those of boundary preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.