Résumé : The Jack superpolynomials are symmetric polynomials, involving commuting and anticommuting variables, that are orthogonal eigenfunctions of a certain integrable model known as the supersymmetric Calogero-Moser-Sutherland model.
We will discuss how the usual properties of the Jack polynomials can be extended to the Jack superpolynomial case. We will mainly focus on the fact that classes of Jack superpolynomials at special values of the coupling constant admit clusters of size at most k, that is, they vanish when k+1 variables are equal but not (conjecturally) when only k are identified (a sort of generalization of the Pauli exclusion principle).
We will also describe the connection between the super-Virasoro algebra and the vanishing of the Jack superpolynomials.

Dernière modification : Monday 27 May 2024

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