For degenerate principal series of GL_n satisfying a balanced condition, the Eisenstein map on the bottom-degree cohomology is Aut(C)-equivariant, yielding a rational structure on this Eisenstein cohomology.
Degenerate principal series representations of GL _n( ) and GL _n( )
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On rationality of certain Eisenstein cohomology
For degenerate principal series of GL_n satisfying a balanced condition, the Eisenstein map on the bottom-degree cohomology is Aut(C)-equivariant, yielding a rational structure on this Eisenstein cohomology.