A Partial Cayley Transform of Siegel-jacobi Disk
نویسنده
چکیده
Let Hg and Dg be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let C be the Euclidean space of all h× g complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk Dg × C (h,g) onto the Siegel-Jacobi space Hg × C (h,g) which gives a partial bounded realization of Hg × C (h,g) by Dg ×C . We prove that the natural actions of the Jacobi group on Dg ×C (h,g) and Hg×C (h,g) are compatible via a partial Cayley transform. A partial Cayley transform plays an important role in computing differential operators on the Siegel-Jacobi disk Dg×C (h,g) invariant under the natural action of the Jacobi group on Dg × C (h,g) explicitly.
منابع مشابه
A PARTIAL CAYLEY TRANSFORM OF Dg × C (h,g)
Let Hg and Dg be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let C be the Euclidean space of all h× g complex matrices. We present a partial Cayley transformation of Dg × C (h,g) onto Hg × C (h,g) which gives a partial bounded realization of Hg × C (h,g) as Dg × C . We prove that the canonical actions of the Jacobi group on Dg × C (h,g) and Hg × C (h,g) a...
متن کاملInvariant Metrics and Laplacians on Siegel-jacobi Disk
Abstract. Let Dn be the generalized unit disk of degree n. In this paper, we find Riemannian metrics on the Siegel-Jacobi disk Dn × C (m,n) which are invariant under the natural action of the Jacobi group explicitly and also compute the Laplacians of these invariant metrics explicitly. These are expressed in terms of the trace form. We give a brief remark on the theory of harmonic analysis on t...
متن کاملSome Results for the Jacobi-Dunkl Transform in the Space $L^{p}(mathbb{R},A_{alpha,beta}(x)dx)$
In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.
متن کاملAdmissible Wavelets on the Siegel Domain of Type One
Let Sp(n,R) be the symplectic group, and K∗ n its maximal compact subgroup. Then G = Sp(n,R)/K∗ n can be realized as the Siegel domain of type one. The square-integrable representation of G gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent s...
متن کاملCayley transforms in micromagnetics
Methods of numerical integration of ordinary differential equations exploiting the Cayley transform arise in a variety of contexts, ranging from the classical mid-point rule to symplectic and (almost) Poisson integrators, to numerical methods on Lie Groups. In earlier work, the first author investigated the interplay between the Cayley transform and the Jacobi identity in establishing certain e...
متن کامل