Integrality and Specialized Symmetric Functions

2025/08/11 by Berele, Allan
#05E05 (Secondary) #16R30 (primary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.08018

Abstract

Given d₁,…,d_k in the field F, there is a weighted trace function F^k→ F given by tr(x₁,…,x_k)=∑ d_ix_i. We prove that F^k satisfies trace identities of the forms α(d₁,…,d_k) x^N= a linear combination of terms with lower powers of x; and tr(y₁)⋯ tr(y_n)= a linear combination of terms with fewer traces. The approach uses specialized symmetric functions.

Citations

• J-trace identities and invariant theory

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