Computer Condensation of Modular Representations

Condensation replaces an explicit matrix representation of a group by a related but much smaller representation of a Hecke algebra. We give a general account of condensation and show how condensation is used to obtain the structure of large matrix representations. We include a detailed description of a new implementation of condensation. As an example of condensation, we work through the stages of the computation of the 2-modular character table of G"2(3).