
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.
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
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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