From Jack to Double Jack Polynomials via the Supersymmetric Bridge

摘要: The Calogero{Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. supersymmetric coun- terpart this model, although much less ubiquitous, has an equally rich structure. In particular, superpolynomials, appear to share very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic fermionic degrees. Now, truly amazing feature pops out when degree is sufficiently large: superpolynomials stabilize factorize. Their stability respect expansion terms elementary basis where, stable sector, coefficients become independent degree. factorization seen variables stripped off suitable way which results product two ordinary polynomials (somewhat modified plethystic transformations), dubbed double Here, addition spelling these results, were first obtained context Macdonal we provide heuristic derivation superpolynomial case performing simple manipulations on eigen-operators, rendering them particles addition, work expression Hamiltonian characterizes Jacks. This Hamiltonian, defines new integrable system, involves not only expected pieces but also combinations generators underlying affine b sl2 algebra.