The transfer in the invariant theory of modular permutation representations

Mara D. Neusel

Vol. 199 (2001), No. 1, 121–135

DOI: 10.2140/pjm.2001.199.121

Abstract

This note investigates the image of the transfer homomorphism for permutation representations of finite groups over finite fields. One obtains a number of results showing that the image of the transfer ℑ(Tr) together with certain Chern classes generate the ring of invariants as an algebra. By a careful analysis of orbit sums one finds the surprising fact that the ideal ℑ(Tr) is a prime ideal for cyclic p-groups and determines an upper bound on its height.

Milestones

Received: 19 August 1998

Revised: 22 April 1999

Published: 1 May 2001