Assembly for a window, a window frame or a shutter comprising an opening sliding in a fixed sash in a direction of sliding (II-II), wherein: - the opening comprises a top crossmember and a bottom crossmember, - the fixed sash comprises: • a top guiding rail comprising a guiding rib intended to be received at least partly by fitting into the top crossmember, • a bottom guiding rail, said bottom guiding rail comprising a rolling rib, - compressible seals are borne by one of the top crossmember or the top guiding rail and by one of the bottom crossmember or the bottom guiding rail, and are intended to be compressed between the opening and the fixed sash by a displacement of the opening transversely to its direction of sliding (II-II), wherein: - on a bottom face of the bottom crossmember there are disposed rolling means intended to roll longitudinally on the rolling rib, said rolling means allowing a displacement of the opening transversely to the direction of sliding (II-II) of the opening, - on the bottom face of the bottom crossmember there are disposed first transverse displacement means comprising bearing means, capable of coming to bear against the rolling rib to provoke a relative displacement of the bottom crossmember relative to the bottom guiding rail transversely to the direction of sliding (II-II) of the opening, - on a top face of the top crossmember there are disposed second transverse displacement means comprising bearing means, capable of coming to bear against the guiding rib to provoke a relative displacement of the top crossmember relative to the top guiding rail transversely to the direction of sliding (II-II) of the opening, and wherein: - the bottom crossmember of the opening comprises a first longitudinal groove in which the rolling means are disposed, and a second longitudinal groove in which the first transverse displacement means are disposed, - the top crossmember of the opening comprises a third longitudinal groove in which the second transverse displacement means are disposed, - the top crossmember of the opening comprises a fourth longitudinal groove conformed in such a way as to at least partly receive the guiding rib upon a translational movement of the opening in the direction of the top guiding rail. - the opening comprises a top crossmember and a bottom crossmember, - the fixed sash comprises: • a top guiding rail comprising a guiding rib intended to be received at least partly by fitting into the top crossmember, • a bottom guiding rail, said bottom guiding rail comprising a rolling rib, • a top guiding rail comprising a guiding rib intended to be received at least partly by fitting into the top crossmember, • a bottom guiding rail, said bottom guiding rail comprising a rolling rib, - compressible seals are borne by one of the top crossmember or the top guiding rail and by one of the bottom crossmember or the bottom guiding rail, and are intended to be compressed between the opening and the fixed sash by a displacement of the opening transversely to its direction of sliding (II-II), - on a bottom face of the bottom crossmember there are disposed rolling means intended to roll longitudinally on the rolling rib, said rolling means allowing a displacement of the opening transversely to the direction of sliding (II-II) of the opening, - on the bottom face of the bottom crossmember there are disposed first transverse displacement means comprising bearing means, capable of coming to bear against the rolling rib to provoke a relative displacement of the bottom crossmember relative to the bottom guiding rail transversely to the direction of sliding (II-II) of the opening, - on a top face of the top crossmember there are disposed second transverse displacement means comprising bearing means, capable of coming to bear against the guiding rib to provoke a relative displacement of the top crossmember relative to the top guiding rail transversely to the direction of sliding (II-II) of the opening, - the bottom crossmember of the opening comprises a first longitudinal groove in which the rolling means are disposed, and a second longitudinal groove in which the first transverse displacement means are disposed, - the top crossmember of the opening comprises a third longitudinal groove in which the second transverse displacement means are disposed, - the top crossmember of the opening comprises a fourth longitudinal groove conformed in such a way as to at least partly receive the guiding rib upon a translational movement of the opening in the direction of the top guiding rail.