2023/01/30 by Shaul Zemel, Zemel, Shaul
Chemistry · Mathematics · Physics and Astronomy · #05E05 #13A50 #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #perhaps 32W50
paper · pdf · doi:10.48550/arxiv.2302.00549
openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A symmetric function of N variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our original variables, producing a simple form for the associated Weyl algebra. Both our coordinates, and the form of our differential operators at total diagonal points, exhibit interesting properties, and are related to interesting objects like Bell polynomials. They can be modified to give a simple formula for the gradient of our symmetric function at any point.