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 ${\theta }_k$. 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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Cited by in corpus (4)

• Supersymmetric polynomials and algebro-combinatorial duality
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Super-Hamiltonians for super-Macdonald polynomials
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations