Branching of Modular Representations of the Alternating Groups

Based on Kleshchevʹs branching theorems for thep-modular irreducible representations of the symmetric group and on the recent proof of the Mullineux Conjecture, we investigate in this article the corresponding branching problem for thep-modular irreducible representations of the alternating groupAn. We obtain information on the socle of the restrictions of suchAn-representations toAn − 1as well as on the multiplicities of certain composition factors; furthermore, irreducibleAn-representations with irreducible restrictions toAn − 1are studied.