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

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

1994-05-05

arxiv.org/abs/hep-th/9405038v2

J.Math.Phys. 36 (1995) 1645-1651

Physics

High Energy Physics

High Energy Physics - Theory

6 pages. One reference ([FF]) has been corrected. New references and an introduction have been added

Scientific paper

10.1063/1.531076

We derive explicit integral formulas for eigenfunctions of quantum integrals of the Calogero-Sutherland-Moser operator with trigonometric interaction potential. In particular, we derive explicit formulas for Jack's symmetric functions. To obtain such formulas, we use the representation of these eigenfunctions by means of traces of intertwining operators between certain modules over the Lie algebra $\frak gl_n$, and the realization of these modules on functions of many variables.

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