On the representations of Sp(p,q) and SO^\ast(2n) unitarily induced from derived functor modules

Abstract

We obtain a decomposition formula of a representation of Sp(p,q) and SO^\ast(2n) unitarily induced from a derived functor module, which enables us to reduce the problem of irreducible decompositions to the study of derived functor modules. In particular, we show such an induced representation is decomposed into a direct sum of irreducible unitarily induced modules from derived functor modules under some regularity condition on the parameters. In particular, representations of SO^\ast(2n) and Sp(p,q) induced from one-dimensional unitary representations of their parabolic subgroups are irreducible.