Separating invariants over finite fields

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Kemper, Gregor²  Lopatin, Artem¹  Reimers, Fabian² 

[1] Univ Estadual Campinas, 651 Sergio Buarque Holanda, BR-13083859 Campinas, SP, Brazil

[2] Tech Univ Munich, Zentrum Math M11, Boltzmannstr 3, D-85748 Garching, Germany

关键词: Invariant theory;    Separating invariants;    Generators;    Relations;    Positive characteristic;    Symmetric group;    Multisymmetric polynomials;   

DOI  :  10.1016/j.jpaa.2021.106904

来源: Elsevier

【 摘 要 】

We determine the minimal number of separating invariants for the invariant ring of a matrix group G <= GL(n)(F-q) over the finite field F-q. We show that this minimal number can be obtained with invariants of degree at most vertical bar G vertical bar 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 F-2 for two important representations of the symmetric group. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free