Primitive central idempotents of finite group rings of symmetric groups

Let p be a prime. We denote by S-n the symmetric group of degree n, by A(n) the alternating group of degree n and by F-p the field with p elements. An important concept of modular representation theory of a finite group G is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring F(q)G, where q is a prime power. Here, we describe a new method to compute the primitive central idempotents of FqG for arbitrary prime powers q and arbitrary finite groups G. For the group rings FpSn of the symmetric group, we show how to derive the primitive central idempotents of FpSn-p from the idempotents of FpSn. Improving the theorem of Osima for symmetric groups we exhibit a new subalgebra of FpSn which contains the primitive central idempotents. The described results are most efficient for p = 2. In an appendix we display all primitive central idempotents of F2Sn and F(4)A(n) for n <= 50 which we computed by this method.