The Tilting Tensor Product Theorem and Decomposition Numbers for Symmetric Groups

We show how the tilting tensor product theorem for algebraic groups implies a reduction formula for decomposition numbers of the symmetric group. We use this to prove generalisations of various theorems of Erdmann and of James and Williams. Supported by Nuffield grant scheme NUF-NAL 02. Preliminary work on this paper was undertaken at the Isaac Newton Institute as part of the programme on Symmetric Functions and Macdonald Polynomials.