Lucia Morotti (Hannover)

Irreducible tensor products of representations of symmetric and alternating groups

Abstract:

In general tensor products of irreducible representations of degree greater than 1 are not irreducible. For symmetric groups such irreducible tensor products are only possible in characteristic 2. For alternating groups however there are some such irreducible tensor products in arbitrary characteristic.

In this talk I will give a classification of irreducible tensor products of representations of symmetric and, as far as possible, alternating groups. I will also sketch part of the proof of the classification of irreducible tensor products of representations of symmetric groups (which was first formulated by Gow and Kleshchev as a conjecture).