Work

Supersymmetric polynomials and algebro-combinatorial duality

Year: 2024

Type: article

Abstract: 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 ( 𝔤 𝔩 ̂ 1 | 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.

Source: SciPost Physics

DOI: 10.21468/scipostphys.17.4.119

Authors: Dmitry Galakhov, Alexei Morozov, Nikita Tselousov

Institutions: Kurchatov Institute, Institute of Earthquake Prediction Theory and Mathematical Geophysics, Institute for Information Transmission Problems, Institute for Theoretical and Experimental Physics, Moscow Institute of Physics and Technology

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Russian Foundation for Basic Research, Foundation for the Advancement of Theoretical Physics and Mathematics, Russian Academy of Sciences

Awards: G1344660904, G7822654024