Admissibility for quasiregular representations of exponential solvable Lie groups
Let N be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra of dimension n. Let H be a subgroup of the automorphism group of N. Assume that H is a commutative, simply connected, connected Lie group with Lie algebra . Furthermore, assume that the linear adjoint action of on is diagonalizable with non-purely imaginary eigenvalues. Let . We obtain an explicit direct integral decomposition for τ, including a description of the spectrum as a submanifold of (+)*, and a...