Displaying similar documents to “Classification of connected unimodular Lie groups with discrete series”

Admissibility for quasiregular representations of exponential solvable Lie groups

Vignon Oussa (2013)

Colloquium Mathematicae

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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 τ = I n d H N ⋊ H 1 . We obtain an explicit direct integral decomposition for τ, including a description of the spectrum as a submanifold of...

Transitive riemannian isometry groups with nilpotent radicals

C. Gordon (1981)

Annales de l'institut Fourier

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Given that a connected Lie group G with nilpotent radical acts transitively by isometries on a connected Riemannian manifold M , the structure of the full connected isometry group A of M and the imbedding of G in A are described. In particular, if G equals its derived subgroup and its Levi factors are of noncompact type, then G is normal in A . In the special case of a simply transitive action of G on M , a transitive normal subgroup G ' of A is constructed with dim G ' = dim G and a sufficient condition...

On holomorphically separable complex solv-manifolds

Alan T. Huckleberry, E. Oeljeklaus (1986)

Annales de l'institut Fourier

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Let G be a solvable complex Lie group and H a closed complex subgroup of G . If the global holomorphic functions of the complex manifold X : G / H locally separate points on X , then X is a Stein manifold. Moreover there is a subgroup H ^ of finite index in H with π 1 ( G / H ^ ) nilpotent. In special situations (e.g. if H is discrete) H normalizes H ^ and H / H ^ is abelian.