Unitary representations and a general vanishing theorem for \((0,r)\)- cohomology
A general and precise vanishing theorem for the \((0,r)\)-cohomology of a compact arithmetic quotient of a Hermitian symmetric space \(X=G/K\) (\(G\) a connected non-compact semisimple Lie group) is given. Moreover, the unitary representations of \(G\) which contribute via Matsushima's formula to these cohomology groups are described. These results improve the ones given by the author in his earlier paper [Osaka J. Math. 18, 147-160 (1981; Zbl 0469.32011)].
scientific article; zbMATH DE number 5693