The Fock space representations of the affine quantum Lie algbra of the affine special linear group has its beginnings in physics, but is of great interest in mathematics due to the LLT algorithm, which provides an algorithm for computing decomposition matrices for certain Hecke algebras in characteristic zero. In certain 'nice' situations, it is possible to express this algorithm as an explicit formula.

This Excel spreadsheet gives the decomposition numbers for S_n. These tables are available from a number of sources.