Residue symbols and Jantzen-Seitz partitions

摘要

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 Sn-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. (C) 1998 Academic Press. [References: 18]