# Macdonald polynomials in superspace as eigenfunctions of commuting operators

@article{BlondeauFournier2012MacdonaldPI, title={Macdonald polynomials in superspace as eigenfunctions of commuting operators}, author={Olivier Blondeau-Fournier and Patrick Desrosiers and Luc Lapointe and Pierre Mathieu}, journal={arXiv: Mathematical Physics}, year={2012} }

A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and triangularity relations. Although many superpolynomials were constructed as solutions of highly over-determined system, the existence issue was left open. This is resolved here: we demonstrate that the underlying construction has a (unique) solution. The proof uses, as a starting point, the definition of the…

## 20 Citations

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