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

Pauls E. Gunnells; Mark McConnell

doi:10.1016/S0022-314X(02)00041-0

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

Pauls E. Gunnells, Mark McConnell

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	46-71
Number of pages	26
Journal	Journal of Number Theory
Volume	100
Issue number	1
DOIs	https://doi.org/10.1016/S0022-314X(02)00041-0
State	Published - May 1 2003
Externally published	Yes

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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10.1016/S0022-314X(02)00041-0

Cite this

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title = "Hecke operators and ℚ-groups associated to self-adjoint homogenous cones",

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.",

keywords = "Arithmetic groups, Automorphic forms, Hecke operators, Jordan algebras, Self-adjoint homogenous cones",

author = "Gunnells, {Pauls E.} and Mark McConnell",

note = "Funding Information: We thank Avner Ash and Bob MacPherson for encouragement and support, and thank the referee for a careful reading. P.E.G. thanks Oklahoma State University for its hospitality. We are both grateful to the NSF for support. ",

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T1 - Hecke operators and ℚ-groups associated to self-adjoint homogenous cones

AU - Gunnells, Pauls E.

AU - McConnell, Mark

N1 - Funding Information: We thank Avner Ash and Bob MacPherson for encouragement and support, and thank the referee for a careful reading. P.E.G. thanks Oklahoma State University for its hospitality. We are both grateful to the NSF for support.

PY - 2003/5/1

Y1 - 2003/5/1

N2 - 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.

AB - 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.

KW - Arithmetic groups

KW - Automorphic forms

KW - Hecke operators

KW - Jordan algebras

KW - Self-adjoint homogenous cones

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EP - 71

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

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

Abstract

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