Hecke operators and image-groups associated to self-adjoint homogeneous cones Original Research Article

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over image, and let Γsubset ofG be an appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on image 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.