RESIDUE SYMBOLS AND JANTZEN-SEITZ PARTITIONS

CHRISTINE BESSENRODT JØRN B. OLSSON

Abstract. Jantzen-Seitz partitions are those p-regular partitions of n which label p-modular irreducible representations of the symmetric group S_{n} which remain irreducible when restricted to S_{n−1}; they have recently also been found to be important for certain exactly solvable models in statistical mechanics. In this article we study their combinatorial properties via a detailed analysis of their residue symbols; in particular the p-cores of Jantzen-Seitz partitions are determined.