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Physics Letters B
Article . 2024 . Peer-reviewed
License: CC BY
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zbMATH Open
Article . 2024
Data sources: zbMATH Open
https://dx.doi.org/10.48550/ar...
Article . 2024
License: arXiv Non-Exclusive Distribution
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Macdonald polynomials for super-partitions

Authors: Dmitry Galakhov; Alexei Morozov; Nikita Tselousov;

Macdonald polynomials for super-partitions

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 $θ_k$. 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.

Keywords

High Energy Physics - Theory, FOS: Physical sciences, Relativity and gravitational theory, Mathematical Physics (math-ph), High Energy Physics - Theory (hep-th), Quantum theory, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Representation Theory (math.RT), Mathematical Physics, Mathematics - Representation Theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Top 10%
Green
gold