On the finiteness of the \(L^ 2\)-automorphic cohomology of a flag domain
Let \(D=G/V\) be a flag domain and let \(E_{\pi}\to D\) be a non-degenerate homogeneous vector bundle over D induced by an irreducible representation \(\pi\) of V. If \(\Gamma\subset G\) is a lattice we prove that the \((L^ 2- \Gamma)\)-automorphic cohomology of D with coefficients in \(E_{\pi}\) is finite dimensional. In particular we establish finiteness of \(\Gamma\)- automorphic cohomology of the period matrix domain \(D=S0_ 1(2n,1)/U(n)\). The finiteness question, which heretofore has been open, is posed by \textit{R. O. Wells} jun. and \textit{J. A. Wolf} [Ann. Math., II. Ser. 105, 397-448 (1977; Zbl 0448.32015)].
scientific article; zbMATH DE number 4008815
scientific article