Abstract
We give an explicit description of the inner cohomology of an adèlic locally symmetric space of a given level structure attached to the general linear group of prime rank n with coefficients in a locally constant sheaf of complex vector spaces. We show that for all primes n the inner cohomology vanishes in all degrees for nonconstant sheaves, otherwise the quotient module of the inner cohomology classes that are not cuspidal is trivial in all degrees for primes n=2,3, and for all primes n≥5 the description of the same at degrees where it is nontrivial is given in terms of algebraic Hecke characters.
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