Residue Symbols and Jantzen–Seitz Partitions

Jantzen–Seitz partitions are thosep-regular partitions ofnwhich labelp-modular irreducible representations of the symmetric groupSnwhich remain irreducible when restricted toSn−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 thep-cores of Jantzen–Seitz partitions are determined.