H. Derksen

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20242026

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math.AC2026

Generic orbits, normal bases, and generation degree for fields of rational invariants

Ben Blum-Smith, Harm Derksen

For a faithful linear representation $V$ of a finite group $G$ in coprime characteristic, we show that if the field Noether number $I^_{field}^{2}$ is the minimum $d$ such tha…

math.AC2026

Syzygies of the transfer ideal of the symmetric group

Harm Derksen, Alexandra Pevzner

We consider the modular action of the symmetric group $S_{n}$ on $R = k [x_{1}, \dots, x_{n}]$ when $char (k) = p \leq n$ . We show that the image of the transfer map $R \to R^{S_{n}}$ …

math.AC2025

Tropical Invariants for Permutation Group Actions

Harm Derksen

We consider the action of a permutation group $G$ of order $k$ on the tropical polynomial semiring in $n$ variables. We prove that the sub-semiring of invariant polynomials is fini…

math.AC2024

Bi-Lipschitz Quotient embedding for Euclidean Group actions on Data

Harm Derksen

For the action of the orthogonal group or euclidean group on k-tuples of vectors we construct a bi-Lipschitz embedding from the orbit space into euclidean space.This embedding has…