Les superpolynômes de Jack et le modèle Calogero-Moser-Sutherland N = 2

Authors: Alarie-Vézina, Ludovic
Advisor: Mathieu, Pierre; Lapointe, Luc
Abstract: We present a generalization of the symmetric Jack polynomial, the N = 2 symmetric Jack superpolynomial, and discuss its links with the N = 2 supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (tCMS) model. We first briefly review the theory of symmetric polynomials that leads us to three different definitions of the symmetric Jack polynomials: a combinatorial definition, the Jack polynomial as the eigenfunction of the tCMS model and as the result of the symmetrization of the non-symmetric Jack polynomial. We then do a brief introduction to the theory of symmetric superpolynomials. We also define the symmetric Jack superpolynomials using the superextension of the three aforementioned characterizations. After this introduction, we get to the main matter by defining the symmetric N = 2 superpolynomials. This ultimately results in a definition of the N = 2 Jack superpolynomial. We construct a N = 2 superextension of the tCMS model and find its conserved quantities. The N = 2 Jack superpolynomials are found to be the eigenfunctions of this model. As an auxiliary result, we obtain a conjecture regarding a combinatorial definition of these superpolynomials.
Document Type: Thèse de doctorat
Issue Date: 2017
Open Access Date: 24 April 2018
Permalink: http://hdl.handle.net/20.500.11794/28194
Grantor: Université Laval
Collection:Thèses et mémoires

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