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arXiv · 2508.08018

Integrality and Specialized Symmetric Functions

Allan Berele
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Abstract

Given $d_1,\ldots,d_k$ in the field $F$, there is a weighted trace function $F^k\rightarrow F$ given by $tr(x_1,\ldots,x_k)=\sum d_ix_i$. We prove that $F^k$ satisfies trace identities of the forms $\alpha(d_1,\ldots,d_k) x^N=$ a linear combination of terms with lower powers of $x$; and $tr(y_1)\cdots tr(y_n)=$ a linear combination of terms with fewer traces. The approach uses specialized symmetric functions.

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Allan Berele. 2025-08-11. Integrality and Specialized Symmetric Functions. https://arxiv.org/abs/2508.08018

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