Jack polynomials in superspace

Details Jack polynomials in superspace Jack polynomials in superspace

2002-09-09

arxiv.org/abs/hep-th/0209074v3

Commun.Math.Phys. 242 (2003) 331-360

Physics

High Energy Physics

High Energy Physics - Theory

28 pages. Corrected version of lemme 3 and other minor corrections and 2 new references; version to appear in Commun. Math. Ph

Scientific paper

10.1007/s00220-003-0933-2

This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were constructed. Orthogonal eigenfunctions are now obtained by diagonalizing the first nontrivial element of a bosonic tower of commuting conserved charges not containing this Hamiltonian. Quite remarkably, the expansion coefficients of these orthogonal eigenfunctions in the supermonomial basis are stable with respect to the number of variables. The second and more direct approach amounts to symmetrize products of non-symmetric Jack polynomials with monomials in the fermionic variables. This time, the orthogonality is inherited from the orthogonality of the non-symmetric Jack polynomials, and the value of the norm is given explicitly.

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