Representations of symmetric groups in characteristic p


Given a finite group G, a representation of G over the complex numbers and a prime p, one can define a representation of G in characteristic p by a process of modular reduction. A natural question to ask is which irreducible representations of G remain irreducible in characteristic p. I will talk about how this question is answered when G is a symmetric or alternating group, before going on to describe some work in progress on double covers of symmetric groups. I will try to keep the talk at a very introductory level.