Cuspidal cohomology classes for GL_n(Z)

Abstract

We prove the existence of a cuspidal automorphic representation $\ddot{I}€$ for $G{L}_{79}/\mathbf{Q}$ of level one and weight zero. We construct $\ddot{I}€$ using symmetric power functoriality and a change of weight theorem, using Galois deformation theory. As a corollary, we construct the first known cuspidal cohomology classes in $H^{\ast }(G{L}_n(\mathbf{Z}),\mathbf{C})$ for any $n>1$.

Accepted version, to appear in the Journal of the American Mathematical Society. 12 pages