  The symmetric simple exclusion process (SEP) is a paradigmatic model of
diffusion in a single-file geometry, in which the particles cannot cross. In
this model, the study of currents have attracted a lot of attention. In
particular, the distribution of the integrated current through the origin, and
more recently, of the integrated current through a moving reference point, have
been obtained in the long time limit. This latter observable is particularly
interesting, as it allows to obtain the distribution of the position of a
tracer particle. However, up to now, these different observables have been
considered independently. Here, we characterise the joint statistical
properties of these currents, and their correlations with the density of
particles. We show that the correlations satisfy closed integral equations,
which generalise the ones obtained recently for a single observable. We also
obtain boundary conditions verified by these correlations, which take a simple
physical form for any single-file system. As a consequence of our results, we
quantify the correlations between the displacement of a tracer, and the
integrated current of particles through the origin.
