2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107290The quantization procedure for both N=1 and N=2 supersymmetric Korteweg-de Vries (SUSY KdV) hierarchies is constructed. Namely, the quantum counterparts of the monodromy matrices, built by means of the integrated vertex operators, are shown to satisfy a specialization of reflection equation, leading to the quantum integrable theory. The relation of such models to the study of integrable perturbed superconformal and topological models is discussed.LaTeX2e, 20 pages, in Problems of Mathematical Physics and Applied Mathematics, Ioffe Physical-Technical Institute, St. Petersburg, 2006, pp. 80-100; N=2 case is based on Quantization of N=2 supersymmetric KdV Hierarchy, Theor. Math. Phys., in press, 2006High Energy Physics - TheoryMathematical PhysicsQuantum Algebratext