# Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation

@article{Atai2021SuperMacdonaldPO,
title={Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation},
author={Farrokh Atai and Martin A. Halln{\"a}s and Edwin Langmann},
journal={arXiv: Quantum Algebra},
year={2021}
}
• Published 12 March 2021
• Mathematics
• arXiv: Quantum Algebra
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald-Ruijsenaars operators introduced by the same authors. We introduce a Hermitian form on the algebra spanned by the super-Macdonald polynomials, prove their orthogonality, compute their (quadratic) norms explicitly, and establish a corresponding Hilbert space interpretation of the super…
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