A Matrix Approach to the Rational Invariants of Certain Classical Groups over Finite Fields of Characteristic Two

Abstract

Let ${\mathbb{F}}_q$ be a finite field of characteristic two and ${\mathbb{F}}_q(X_1,...,X_n)$ a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and pseudo-symplectic groups on ${\mathbb{F}}_q(X_1,...,X_n)$ over ${\mathbb{F}}_q$.

20 pages