Endomorphism rings of permutation modules over maximal Young subgroups

Let K be a field of characteristic two, and let), be a two-part partition of some natural number r. Denote the permutation module corresponding to the (maximal) Young subgroup Sigma(lambda) in Sigma(r) by M-lambda. We construct a full set of orthogonal primitive idempotents of the centraliser subalgebra S-K (lambda) = l(lambda) S-K (2, r) l(lambda) End(K) Sigma(r) (M-lambda) of the Schur algebra S-K (2, r). These idempotents are naturally in one-to-one correspondence with the 2-Kostka numbers. (C) 2006 Elsevier Inc. All rights reserved.