The Image of the Enveloping Algebra and Irreducibility of Induced Representations of Exponential Lie Groups

摘要

It is shown that the image of the universal enveloping algebra of the Lie algebra of an exponential Lie group under a representation of the group induced from a character satisfying the Pukanszky condition is a dense algebra of differential operators. This result is used to prove irreducibility of certain families of nonunitary induced representations of exponential Lie groups.