Relations between permutation representations in positive characteristic
Abstract
Given a finite group G and a field F, a G-set X gives rise to an F[G]-permutation module F[X]. This defines a map from the Burnside ring of G to its representation ring over F. It is an old problem in representation theory, with wide-ranging applications in algebra, number theory, and geometry, to give explicit generators of the kernel K_F(G) of this map, i.e. to classify pairs of G-sets X, Y such that F[X] is isomorphic to F[Y]. When F has characteristic 0, a complete description of K_F(G) is now known. In this paper, we give a similar description of K_F(G) when F is a field of characteristic p>0 in all but the most complicated case, which is when G has a subquotient that is a non-p-hypo-elementary (p,p)-Dress group.
Cite
@article{arxiv.1709.10031,
title = {Relations between permutation representations in positive characteristic},
author = {Alex Bartel and Matthew Spencer},
journal= {arXiv preprint arXiv:1709.10031},
year = {2019}
}
Comments
18 pages; minor corrections and improvements. Final version to appear in Bull. London Math. Soc