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

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

1998-11-23

arxiv.org/abs/math/9811133v2

Mathematics

Number Theory

25 pages, 10 figures, uses psfrag.sty; authors names omitted from first version

Scientific paper

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let G' be an appropriate neat arithmetic subgroup of G. We present two algorithms to compute the action of the Hecke operators on the integral cohomology of G'. This simultaneously generalizes the modular algorithm of Ash-Rudolph to a larger class of groups, and provides techniques to compute the Hecke-module structure of previously inaccessible cohomology groups.

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