Separating invariants over finite fields

Abstract

We determine the minimal number of separating invariants for the invariant ring of a matrix group $G<{\mathrm{GL}}_n({\mathbb{F}}_q)$ over the finite field ${\mathbb{F}}_q$. 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 ${\mathbb{F}}_2$ for two important representations of the symmetric group

18 pages

References in corpus (3)

• Characteristic free description of semi-invariants of $2\times 2$ matrices
• Separating invariants for multisymmetric polynomials
• Separating invariants of three nilpotent 3x3 matrices

Cited by in corpus (2)

• Separating G_2-invariants of several octonions
• Classification of G_2-orbits for pairs of octonions