A holomorphic representation of the multidimensional Jacobi algebra

Abstract

We present a holomorphic representation of the Jacobi algebra ${\mathfrak{h}}_n⋊\mathfrak{sp}(n,\mathbb{R})$ 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.

26 pages, To appear in the Proceedings of the Third Operator Algebras and Mathematical Physics Conference, Bucharest, Romania, August 10 -- 17, 2005, corrected typos

References in corpus (6)

• A holomorphic representation of the multidimensional Jacobi algebra
• Realization of coherent state Lie algebras by differential operators
• Differential operators on orbits of coherent states
• Finite-dimensional Lie subalgebras of the Weyl algebra
• Geometrical phases on hermitian symmetric spaces
• Linear Hamiltonians on homogeneous Kähler manifolds of coherent states

Cited by in corpus (1)

• A holomorphic representation of the multidimensional Jacobi algebra