On cores of partitions and character separation
by
Christine Bessenrodt
Universität Hannover

Partitions and their p-cores play an important rôle in additive number theory and combinatorics, and on the algebraic side, in the p-modular representation theory of the symmetric groups and related groups (in the case when p is a prime) as well as in the representation theory of Hecke algebras. I will report on the investigation of the question whether a partition of n (or a bar partition, respectively) is characterized by all or even just a few of its p-cores (or p-bar cores, resp.), for primes p £ n. In character theoretic terms, this asks for a separation of any two ordinary characters of the symmetric group S_n (or spin characters of their double covers, resp.) by p-blocks, where p £ n are suitable primes. In recent joint work with G. Malle and J. Olsson, we have studied this separation problem not only for the symmetric and alternating groups and their covers, but also for groups of Lie type and sporadic groups (for a general finite group, a suitable selection of prime divisors p of the group order is required for the character separation).

Date received: March 14, 2005