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.

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