Residue symbols and Jantzen-Seitz partitions 

Christine Bessenrodt and Joern B. Olsson 

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.