Twisted Actions of Symmetric Groups
Journal
Journal of Algebra
Journal Volume
188
Journal Issue
2
Pages
626-647
Date Issued
1997
Author(s)
Abstract
LetKbe any field and the symmetric groupSnact on the rational function fieldK(x1,...,xn) by σ(xi)xσ(i)if σ∈Anand σ(xi)xσ(i)-1if σ∉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⊕ni=1K·xiare valid. © 1997 Academic Press.
Type
journal article