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Orthogonality of Jack polynomials in superspace |
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| Authors: | Patrick Desrosiers Luc Lapointe |
| Institution: | a Department of Mathematics and Statistics, The University of Melbourne, Parkville, Australia, 3010 b Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile c Département de physique, de génie physique et d'optique, Université Laval, Québec, Canada, G1K 7P4 |
| Abstract: | Jack polynomials in superspace, orthogonal with respect to a “combinatorial” scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to an “analytical” scalar product, introduced in P. Desrosiers, L. Lapointe, P. Mathieu, Jack polynomials in superspace, Comm. Math. Phys. 242 (2003) 331-360] as eigenfunctions of a supersymmetric quantum mechanical many-body problem. The results of this article rely on generalizing (to include an extra parameter) the theory of classical symmetric functions in superspace developed recently in P. Desrosiers, L. Lapointe, P. Mathieu, Classical symmetric functions in superspace, J. Algebraic Combin. 24 (2006) 209-238]. |
| Keywords: | primary 05E05 secondary 81Q60 33D52 |
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