Les vecteurs singuliers de l'algèbre superconforme dans le secteur de Ramond en termes de superpolynômes de Jack
|Abstract:||This mémoire presents results concerning the Ramond singular vectors of the superconformal algebra. An explicit formula has been obtained for the Ramond singular vectors of the superconformal algebra via its superpolynomial representation and the formula is given here in terms of Jack superpolynomials. We first present some basic elements of the integer partition and symmetric functions theories. This leads us to consider the eigenfunctions of the Calogero-Sutherland (CS) model, the Jack polynomials. These happen to be the singular vectors of the conformal algebra when represented in terms of symmetric polynomials. Given those results, we extend the CS model to the supersymmetric case and interpret its eigenfunctions as the Jack superpolynomials which are symmetric functions in superspace. We then display the explicit formula of the Ramond singular vectors of the superconformal algebra which has been obtained in terms of Jack superpolynomials.|
|Document Type:||Mémoire de maîtrise|
|Open Access Date:||20 April 2018|
|Collection:||Thèses et mémoires|
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