Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra

Details Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra

1995-03-07

arxiv.org/abs/hep-th/9503043v4

Nucl.Phys. B449 (1995) 347-374

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 29 pages, 2 figures, New sections for skew-Jack polynomial and example of singular vectors added

Scientific paper

10.1016/0550-3213(95)00286-2

Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the $W_N$ algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral representations of the skew-Jack polynomials.

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