Integral formulas for wave functions of quantum many-body problems and representations of 𝔤l n

Abstract

Explicit integral formulas are derived for eigenfunctions of quantum integrals of the Calogero–Sutherland–Moser operator with a trigonometric interaction potential. In particular, explicit formulas for Jack’s symmetric functions are derived. To obtain such formulas, one must use the representation of these eigenfunctions by means of traces of intertwining operators between certain modules over the Lie algebra 𝔤ln, and the realization of these modules on functions of many variables.