Symmetric polynomials in the symplectic alphabet and their expression via Dickson--Zhukovsky variables

Per Alexandersson, Luis Angel González-Serrano, Egor A. Maximenko +1

Given a symmetric polynomial $P$ in $2n$ variables, there exists a unique symmetric polynomial $Q$ in $n$ variables such that \[ P(x_1,\ldots,x_n,x_1^{-1},\ldots,x_n^{-1}) =Q(x_1+x…