Macdonald polynomials for super-partitions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911981517144064 |
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| author | Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita |
| author_facet | Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita |
| contents | 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 $θ_k$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Macdonald polynomials for super-partitions Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory 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 $θ_k$. 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. |
| title | Macdonald polynomials for super-partitions |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2407.03301 |