The Calogero-Sutherland model occurs in a large number of physical contexts,either directly or via its eigenfunctions, the Jack polynomials. Thesupersymmetric counterpart of this model, although much less ubiquitous, has anequally rich structure. In particular, its eigenfunctions, the Jacksuperpolynomials, appear to share the very same remarkable combinatorial andstructural properties as their non-supersymmetric version. Thesesuper-functions are parametrized by superpartitions with fixed bosonic andfermionic degrees. Now, a truly amazing feature pops out when the fermionicdegree is sufficiently large: the Jack superpolynomials stabilize andfactorize. Their stability is with respect to their expansion in terms of anelementary basis where, in the stable sector, the expansion coefficients becomeindependent of the fermionic degree. Their factorization is seen when thefermionic variables are stripped off in a suitable way which results in aproduct of two ordinary Jack polynomials (somewhat modified by plethystictransformations), dubbed the double Jack polynomials. Here, in addition tospelling out these results, which were first obtained in the context ofMacdonal superpolynomials, we provide a heuristic derivation of the Jacksuperpolynomial case by performing simple manipulations on the supersymmetriceigen-operators, rendering them independent of the number of particles and ofthe fermionic degree. In addition, we work out the expression of theHamiltonian which characterizes the double Jacks. This Hamiltonian, whichdefines a new integrable system, involves not only the expectedCalogero-Sutherland pieces but also combinations of the generators of anunderlying affine ${\widehat{\mathfrak {sl}}_2}$ algebra.
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