2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135940In this paper, we use the unitary representation theory of $SL_2(\mathbb R)$ to understand the Rankin-Cohen brackets for modular forms. Then we use this interpretation to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.Quantum AlgebraCombinatoricstext