On systems of Hecke eigenvalues in cohomology of certain subgroups of GL_n(F)

Details On systems of Hecke eigenvalues in cohomology of certain subgroups of GL_n(F) On systems of Hecke eigenvalues in cohomology of certain subgroups of GL_n(F)

2008-10-10

arxiv.org/abs/0810.1814v1

Mathematics

Number Theory

12 pages

Scientific paper

We show how there is a natural action on the cohomology groups attached to certain subgroups of GL_n(F) of the Hecke operators defined as elements in an adelic double coset algebra. Our main result is, that if a system of eigenvalues for Hecke operators occur in the cohomology groups with coefficients in certain modules, then by changing the groups the system also occur in the cohomology groups with coefficients in a 1-dimensional module.

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