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

Pauls E. Gunnells, Mark McConnell

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)46-71
Number of pages26
JournalJournal of Number Theory
Volume100
Issue number1
DOIs
StatePublished - May 1 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Arithmetic groups
  • Automorphic forms
  • Hecke operators
  • Jordan algebras
  • Self-adjoint homogenous cones

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