Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over ℚ, and let Γ ⊂ G be an appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on Hi(Γ; ℤ) 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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Arithmetic groups
- Automorphic forms
- Hecke operators
- Jordan algebras
- Self-adjoint homogenous cones