Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu

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Admissibility for quasiregular representations of exponential solvable Lie groups

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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...

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Lie groups with smooth characters and with smooth semicharacters

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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...

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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 $\hat{H}$ of finite index in $H$ with $π_{1} (G / \hat{H})$ nilpotent. In special situations (e.g. if $H$ is discrete) $H$ normalizes $\hat{H}$ and $H / \hat{H}$ is abelian.

Type I criteria and the Plancherel formula for Lie groups with co-compact radical

Ronald L. Lipsman (1982)

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