Orthogonality of Jack polynomials in superspace

• Autores: Patrick Desrosiers, Luc Lapointe, Pierre Mathieu
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 1, 2007, págs. 361-388
• Idioma: inglés
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• Resumen

  • 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].