Bargmann-Type Finite-Dimensional Reductions of the Lax-Integrable Supersymmetric Boussinesq Hierarchy and Their Integrability

Abstract

For the supersymmetric Boussinesq hierarchy connected with the Lax-type flows on the space dual to the Lie algebra of superintegrodifferential operators of one anticommuting variable for some nonself-adjoint superdifferential operator, we develop the method of Bargmann-type finite-dimensional reductions. We establish the existence of an exact even supersymplectic structure on the corresponding invariant finite-dimensional supersubspace of the supersymmetric Boussinesq hierarchy, as well as the Lax–Liouville integrability of commuting vector fields, generated by the hierarchy and reduced to this supersubspace.