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

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