2019/03/18 by Ludovic Alarie-Vezina, Ludovic Alarie-Vézina, Olivier Blondeau-Fournier +8 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.CO #math.MP
paper · pdf · doi:10.48550/arxiv.1903.07777
38 pages
arxiv created 2019/03/19 · openalex publication_date 2019/03/19 · arxiv updated 2019/03/20 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We present a review of the most important results in the theory of symmetric functions in superspace (or symmetric superpolynomials), summarizing all principal contributions since its introduction in 2001 in the context of the supersymmetric Calogero-Moser-Sutherland integrable model. We also mention some open problems which remain unanswered at this moment, in particular the connection with representation theory. In addition, we provide a free open access source code, relying on SageMath library, that can be used as a research tool for symmetric superpolynomials. The content is directed to an audience new to this research area, but who is familiar with the classical theory of symmetric functions.