Stacey Law, University of Cambridge: Linear characters of Sylow subgroups of the symmetric group

Let p be an odd prime and n a natural number. We determine the irreducible constituents of the permutation module induced by the action of the symmetric group S_n on the cosets of a Sylow p-subgroup P_n . In the course of this work, we also prove a symmetric group analogue of a well-known result of Navarro for p-solvable groups on a conjugacy action of N_G(P ). Before describing some consequences of these results, we will give an overview of the background and recent related results in the area.