相关论文: Bergman representative coordinates on the Siegel-J…

The coherent state representation of the Jacobi group $G^J_1$ is indexed with two parameters, $\mu (=\frac{1}{\hbar})$, describing the part coming from the Heisenberg group, and $k$, characterizing the positive discrete series…

We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel-Jacobi disk are obtained. The scalar holomorphic discrete…

We show that the Wei-Norman method applied to describe the evolution on the Siegel-Jacobi disk $\mathcal{D}^J_1=\mathcal{D}_1\times\mathbb{C}^1$, where $\mathcal{D}_1$ denotes the Siegel disk, determined by a hermitian Hamiltonian linear in…

We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the…

We consider mixed normed Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper we compare the results available in the…

Let ${\mathbb H}_g$ and ${\mathbb D}_g$ be the Siegel upper half plane and the generalized unit disk of degree $g$ respectively. Let ${\mathbb C}^{(h,g)}$ be the Euclidean space of all $h\times g$ complex matrices. We present a partial…

For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$…

The real Jacobi group $G^J_1(\mathbb{R})={\rm SL}(2,\mathbb{R})\ltimes {\rm H}_1$, where ${\rm H}_1$ denotes the 3-dimensional Heisenberg group, is parametrized by the $S$-coordinates $(x,y,\theta,p,q,\kappa)$. We show that the parameter…

The Siegel-Jacobi space is a non-symmetric homogeneous space which is very important geometrically and arithmetically. In this short paper, we propose the basic problems in the geometry of the Siegel-Jacobi space.

In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic creation operators while the partial derivatives $\partial_{z^j}$ act as annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional bosonic…

The Siegel-Jacobi space is a non-symmetric homogeneous space which is very important geometrically and arithmetically. In this paper, we discuss the theory of the geometry and the arithmetic of the Siegel-Jacobi space.

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of…

We find the homogenous K\"ahler isomorphism $FC$ which expresses the K\"ahler two-form on the Siegel-Jacobi domain $\mathcal{D}^J_1=\mathbb{C}\times\mathcal{D}_1$ as the sum of the K\"ahler two-form on $\mathbb{C}$ and the one on the Siegel…

We show that the ring of Siegel-Jacobi forms of fixed degree and of fixed or bounded ratio between weight and index is not finitely generated. Our main tool is the theory of toroidal b-divisors and their relation to convex geometry. As a…

In this paper, we investigate the $\partial$-complex on weighted Bergman spaces on Hermitian manifolds satisfying a certain holomorphicity/duality condition. This generalizes the situation of the Segal-Bargmann space in $\mathbb{C}^n$,…

We consider a bounded domain $\Omega \subseteq \mathbb C^d$ which is a $G$-space for a finite complex reflection group $G$. For each one-dimensional representation of the group $G,$ the relative invariant subspace of the weighted Bergman…

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 restricted Siegel disc is a homogeneous space related to the connected component $T_0(1)$ of the Universal Teichm\"uller space via the period mapping. In this paper we show that it is a coadjoint orbit of the universal central extension…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil…