Macdonald polynomials for super-partitions

Galakhov, Dmitry; Morozov, Alexei; Tselousov, Nikita

doi:10.1016/j.physletb.2024.138911

Physics Letters B

2024

DOI: 10.1016/j.physletb.2024.138911

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Macdonald polynomials for super-partitions

Dmitry Galakhov,

Alexei Morozov,

Nikita Tselousov

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2024

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Supersymmetric polynomials and algebro-combinatorial duality

Galakhov,

Morozov,

Tselousov

2024

SciPost Phys.

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In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend on odd Grassmann variables as well. Members of these families are labeled by respective modifications of Young diagrams. We show that the super-Macdonald polynomials form a representation of a super-algebra analog \mathsf{T}(\widehat{\mathfrak{gl}}_{1|1})𝖳(𝔤𝔩̂1|1) of Ding-Iohara-Miki (quantum toroidal) algebra, emerging as a BPS algebra of D-branes on a conifold. A supersymmetric modification for Young tableaux and Kostka numbers are also discussed.

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Supersymmetric polynomials and algebro-combinatorial duality

Galakhov,

Morozov,

Tselousov

2024

SciPost Phys.

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Macdonald polynomials for super-partitions

Cited by 1 publication

References 33 publications

Supersymmetric polynomials and algebro-combinatorial duality

Supersymmetric polynomials and algebro-combinatorial duality

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