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
โฆ LIBER โฆ
Nontriviality of the space of holomorphically induced representations of a solvable Lie group
โ Scribed by A. A. Zaitsev
- Publisher
- Springer US
- Year
- 1977
- Tongue
- English
- Weight
- 180 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 (