Hepler, Charles Thomas2008-02-262008-02-261994-10-01http://hdl.handle.net/1880/45530This thesis examines the computational complexity of the problem of finding the characters of finite groups and some associated problems. The central focus is how the complexity changes according to how the group is specified. We examine two extremes. Considering computations from Cayley tables, when the input size is quadratic in the order of the input group, we observe that we can efficiently invert Burnside's character table algorithm to find class matrices. We also consider computations involving the symmetric group with inputs of size polylogarithmic in the order of the input group. We show completeness and hardness results for computations of individual characters of the symmetric group. Examining the problem of decomposition of outer products of characters of the symmetric group, we show that a generalization of the problem is computationally hard. We show that lattice partitions can be enumerated efficiently.EngComputer Scienceunknown1994-545-1410.11575/PRISM/30819