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In the framework of the algebraic approach to form factors in two-dimensionalintegrable models of quantum field theory we consider the reduction of thesine-Gordon model to the $\Phi_{13}$-perturbation of minimal conformal modelsof the $M(2,2s+1)$ series. We find in an algebraic form the condition ofcompatibility of local operators with the reduction. We propose a constructionthat make it possible to obtain reduction compatible local operators in termsof screening currents. As an application we obtain exact multiparticle formfactors for the compatible with the reduction conserved currents $T_{\pm2k}$,$\Theta_{\pm(2k-2)}$, which correspond to the spin $\pm(2k-1)$ integrals ofmotion, for any positive integer~$k$. Furthermore, we obtain all form factorsof the operators $T_{2k}T_{-2l}$, which generalize the famous $T\bar T$operator. The construction is analytic in the $s$ parameter and, therefore,makes sense in the sine-Gordon theory.

Form factors of descendant operators: Reduction to perturbed $M(2,2s+1)$ models