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Representations of solvable Lie groups

โœ Scribed by I. M. Shchepochkina

Publisher
Springer US
Year
1977
Tongue
English
Weight
214 KB
Volume
11
Category
Article
ISSN
0016-2663

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Using a parametrization for the universal covering \(c_{10}\) of any coadjoint orbit \(c\) of a solvable (connected and simply connected) Lie group \(G\), we prove that the Moyal product on \(\mathfrak{c}_{0}\) gives a realization of the unitary representations canonically associated to the orbit (

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We generalize a result about two-step nilpotent Lie groups by Carolyn Gordon and He Ouyang: Let \(\left\{\Gamma_{t}\right\}_{1 \geqslant 0}\) be a continuous family of uniform discrete subgroups of a simply connected Lie group \(G\) such that the quasi-regular representations of \(G\) on \(L^{2}\lef

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We study holomorphically induced representations r of Lie groups G=exp g from weak polarizations h at f ยฅ g\*. When G is a connected and simply connected Lie group whose Lie algebra is a normal j-algebra, we obtain a sufficient condition for non-vanishing of r and the decomposition of r into irreduc