  The Calogero-Sutherland model occurs in a large number of physical contexts,
either directly or via its eigenfunctions, the Jack polynomials. The
supersymmetric counterpart of this model, although much less ubiquitous, has an
equally rich structure. In particular, its eigenfunctions, the Jack
superpolynomials, appear to share the very same remarkable combinatorial and
structural properties as their non-supersymmetric version. These
super-functions are parametrized by superpartitions with fixed bosonic and
fermionic degrees. Now, a truly amazing feature pops out when the fermionic
degree is sufficiently large: the Jack superpolynomials stabilize and
factorize. Their stability is with respect to their expansion in terms of an
elementary basis where, in the stable sector, the expansion coefficients become
independent of the fermionic degree. Their factorization is seen when the
fermionic variables are stripped off in a suitable way which results in a
product of two ordinary Jack polynomials (somewhat modified by plethystic
transformations), dubbed the double Jack polynomials. Here, in addition to
spelling out these results, which were first obtained in the context of
Macdonal superpolynomials, we provide a heuristic derivation of the Jack
superpolynomial case by performing simple manipulations on the supersymmetric
eigen-operators, rendering them independent of the number of particles and of
the fermionic degree. In addition, we work out the expression of the
Hamiltonian which characterizes the double Jacks. This Hamiltonian, which
defines a new integrable system, involves not only the expected
Calogero-Sutherland pieces but also combinations of the generators of an
underlying affine ${\widehat{\mathfrak {sl}}_2}$ algebra.
