Separating invariants over finite fields

Gregor Kemper, Artem Lopatin, Fabian Reimers

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We determine the minimal number of separating invariants for the invariant ring of a matrix group G≤GLn(Fq) over the finite field Fq. We show that this minimal number can be obtained with invariants of degree at most |G|n(q−1). In the non-modular case this construction can be improved to give invariants of degree at most n(q−1). As examples we study separating invariants over the field F2 for two important representations of the symmetric group.

Original languageEnglish
Article number106904
JournalJournal of Pure and Applied Algebra
Volume226
Issue number4
DOIs
StatePublished - Apr 2022

Keywords

  • Generators
  • Invariant theory
  • Multisymmetric polynomials
  • Positive characteristic
  • Relations
  • Separating invariants
  • Symmetric group

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