SciPost Submission Page
Supersymmetric polynomials and algebro-combinatorial duality
by Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
Submission summary
| Authors (as registered SciPost users): | Dmitry Galakhov |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2407.04810v1 (pdf) |
| Date submitted: | 2024-07-12 16:19 |
| Submitted by: | Galakhov, Dmitry |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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 $\mathsf{T}(\widehat{\mathfrak{gl}}_{1|1})$ of Ding-Ioahara-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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing