Hecke operators and Q-groups associated to self-adjoint homogeneous cones

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over , and let ΓG be an appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph (Invent. Math. 55 (1979) 241) to a larger class of groups, and proposes techniques to compute the Hecke-module structure of previously inaccessible cohomology groups