Separating invariants over finite fields

Author(s)

Kemper, Gregor ^[1] ; Lopatin, Artem ^[2] ; Reimers, Fabian ^[1]

Affiliation

^[1] Tech Univ Munich, Zentrum Math M11, Boltzmannstr 3, D-85748 Garching - Germany

^[2] Univ Estadual Campinas, 651 Sergio Buarque Holanda, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 226, n. 4 APR 2022.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 19/10821-8 - Separating invariants of classical groups
• Grantee: Artem Lopatin
• Support Opportunities: Scholarships abroad - Research