Macdonald polynomials for super-partitions

Fuente: arXiv
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Hauptverfasser: Galakhov, Dmitry, Morozov, Alexei, Tselousov, Nikita
Format: Preprint
Veröffentlicht: 2024
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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