TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.119
TI  - Supersymmetric polynomials and algebro-combinatorial duality
PY  - 2024/10/24
UR  - https://scipost.org/SciPostPhys.17.4.119
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 119
A1  - Galakhov, Dmitry
AU  - Morozov, Alexei
AU  - Tselousov, Nikita
AB  - 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 $\mathsf{T}(\widehat{\mathfrak{gl}}_{1|1})$ 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.
ER  -

@Article{10.21468/SciPostPhys.17.4.119,
	title={{Supersymmetric polynomials and algebro-combinatorial duality}},
	author={Dmitry Galakhov and Alexei Morozov and Nikita Tselousov},
	journal={SciPost Phys.},
	volume={17},
	pages={119},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.119},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.119},
}