INVARIANT-THEORY AND STEENROD OPERATIONS - MAPS BETWEEN RINGS OF INVARIANTS

Let G', G '' be finite groups and rho' : G hooked right arrow GL(n', Q ), rho '' : G '' hooked right arrow GL(n '', Q) faithful rational repr esentations. If T : V' = Q(n') --> Q(n '') = V '' is a linear transfor mation and xi : G' --> G '' a function such that T(g'v') = xi(g') T(v '') For All v' is an element of V', g' is an element of G' then there are induced algebra homomorphisms Q[V ''] --> Q[V'] and Q[V ''](G '') --> Q[V'](G') making the diagram [GRAPHICS] commute. In this note we i solate the invariant theory portion of [1] an extend it to provide a n ecessary and sufficient condition that an algebra homomorphism between rings of invariants Q[V ''](G '') --> Q[V](G') arises in this way.