Twisted Actions of Symmetric Groups Original Research Article

LetKbe any field and the symmetric groupSnact on the rational function fieldK(x1,…,xn) by σ(xi) colon, equals xσ(i)if σ set membership, variant Anand σ(xi) colon, equals xσ(i)−1if σ negated set membership An. We shall show that the fixed fieldK(x1,…,xn)Snis rational overK. Similar results for actions ofSnon the symmetric powers and exterior powers ofV colon, equals circled plusni = 1K · xiare valid.