A holomorphic representation of the multidimensional Jacobi algebra

Details A holomorphic representation of the multidimensional Jacobi algebra A holomorphic representation of the multidimensional Jacobi algebra

2006-04-18

arxiv.org/abs/math/0604381v2

Mathematics

Differential Geometry

26 pages, To appear in the Proceedings of the Third Operator Algebras and Mathematical Physics Conference, Bucharest, Romania,

Scientific paper

10.1142/S0129055X06002619

We present a holomorphic representation of the Jacobi algebra
$\mathfrak{h}_n\rtimes \mathfrak{sp}(n,\R)$ by first order differential
operators with polynomial coefficients on the manifold $\mathbb{C}^n\times
\mathcal{D}_n$. We construct the Hilbert space of holomorphic functions on
which these differential operators act.

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