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arXiv · 2407.03301

Macdonald polynomials for super-partitions

Dmitry Galakhov·Alexei Morozov·Nikita Tselousov
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Abstract

We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann variables $\theta_k$. Starting from recently defined super-Schur polynomials and exploiting orthogonality relations with triangular decompositions we are able to fully determine super-Macdonald polynomials. These new polynomials have similar properties to canonical Macdonald polynomials -- they respect two different orderings in the set of (super)-Young diagrams simultaneously.

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Dmitry Galakhov, Alexei Morozov, Nikita Tselousov. 2024-07-03. Macdonald polynomials for super-partitions. https://doi.org/10.1016/j.physletb.2024.138911

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