English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In a recent work, we have initiated the theory of N=2 symmetricsuperpolynomials. As far as the classical bases are concerned, this is a ratherstraightforward generalization of the N=1 case. However this construction couldnot be generalized to the formulation of Jack superpolynomials. The origin ofthis obstruction is unraveled here, opening the path for building the desiredJack extension. Those are shown to be obtained from the non-symmetric Jackpolynomials by a suitable symmetrization procedure and an appropriate dressingby the anticommuting variables. This construction is substantiated by thecharacterization of the N=2 Jack superpolynomials as the eigenfunctions of theN=2 supersymmetric version of the Calogero-Sutherland model, for which, as aside result, we demonstrate the complete integrability by displaying theexplicit form of four towers of mutually commuting (bosonic) conservedquantities. The N=2 Jack superpolynomials are orthogonal with respect to theanalytical scalar product (induced by the quantum-mechanical formulation) aswell as a new combinatorial scalar product defined on a suitable deformation ofthe power-sum basis.

The N=2 supersymmetric Calogero-Sutherland model and its eigenfunctions