Integrality and Specialized Symmetric Functions

Allan Berele

paper

Integrality and Specialized Symmetric Functions

arXiv:2508.08018

Abstract

Given $d_{1}, \dots, d_{k}$ in the field $F$ , there is a weighted trace function $F^{k} \to F$ given by $t r (x_{1}, \dots, x_{k}) = \sum d_{i} x_{i}$ . We prove that $F^{k}$ satisfies trace identities of the forms $I^\pm (d_{1}, \dots, d_{k}) x^{N} =$ a linear combination of terms with lower powers of $x$ ; and $t r (y_{1}) \dots t r (y_{n}) =$ a linear combination of terms with fewer traces. The approach uses specialized symmetric functions.