Sign conjugacy classes of the symmetric groups

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson

Irreducible tensor products for symmetric and alternating groups in small characteristics

In characteristic 0 irreducible tensor products of representations of symmetric and alternating groups have been described by Zisser and by Bessenrodt and Kleshchev. In positive characteristic a classification conjecture for such products for symmetric groups was formulated by Gow and Kleshchev. Parts of the conjecture were proved shortly after in papers of Bessenrodt and Kleshchev and of Graham and James. However many cases in characteristic 2 for n even were still open. For alternating groups in characteristics p at least irreducible tensor products have been described in a paper of Bessenrodt and Kleshchev, though not for smaller p. In the submitted papers I consider the still open cases, completing the classification of irreducible tensor products of representations of symmetric and alternating groups up to a certain class of tensor products for alternating groups in characteristic 2

Composition factors of 2-parts spin representations of symmetric groups

Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers