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Semibounded Unitary Representations of Double Extensions of Hilbert–Loop Groups

K. H. Neeb (2014)

Annales de l’institut Fourier

A unitary representation $π$ of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i d π (x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of the Lie algebra $𝔤$ of $G$ . We classify all irreducible semibounded representations of the groups ${\hat{ℒ}}_{φ} (K)$ which are double extensions of the twisted loop group $ℒ_{φ} (K)$ , where $K$ is a simple Hilbert–Lie group (in the sense that the scalar product on its Lie algebra is invariant) and $φ$ is...

Semicharacters and Solvable Lie Croups.

Niels Vigand Pedersen (1980)

Mathematische Annalen

Simple facts about analytic vectors and integrability

M. Flato, J. Simon, H. Snellman, D. Sternheimer (1972)

Annales scientifiques de l'École Normale Supérieure

Singular Holomorphic Representations and Singular Modular Forms.

Hans Plesner Jakobsen, Michael Harris (1982)

Mathematische Annalen

Sous-groupes paraboliques des groupes classiques et séries complémentaires

J. Caillez, J. Oberdoerffer (1982)

Publications du Département de mathématiques (Lyon)

Spectra of elements in the group ring of SU(2)

Alex Gamburd, Dmitry Jakobson, Peter Sarnak (1999)

Journal of the European Mathematical Society

We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of $SU (2)$ , providing an elementary solution of Ruziewicz problem on $S^{2}$ as well as giving many new examples of finitely generated subgroups of $SU (2)$ with an explicit gap. The distribution of the eigenvalues of the elements of the group ring $𝐑 [SU (2)]$ in the $N$ -th irreducible representation of $SU (2)$ is also studied. Numerical experiments indicate that for a generic (in measure) element of $𝐑 [SU (2)]$ , the “unfolded” consecutive spacings...

Spinc-quantization and the K-multiplicities of the discrete series

Paul-Émile Paradan (2003)

Annales scientifiques de l'École Normale Supérieure

Square-integrability of tensor products.

Mayer, Matthias (1999)

Journal of Lie Theory

Strong spectral gaps for compact quotients of products of $PSL (2, ℝ)$ )

Dubi Kelmer, Peter Sarnak (2009)

Journal of the European Mathematical Society

The existence of a strong spectral gap for quotients $Γ ∖ G$ of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the Ramanujan–Selberg conjectures. If $G$ has no compact factors then for general lattices a spectral gap can still be established, but there is no uniformity and no effective bounds are known. This note is concerned with the spectral gap for an irreducible...