Year: 2023
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Zemel, Shaul
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4319050294