Invariant metrics and Laplacians on Siegel-Jacobi Disk

Abstract

Let ${\mathbb{D}}_n$ be the generalized unit disk of degree $n$. In this paper, we find Riemannian metrics on the Siegel-Jacobi disk ${\mathbb{D}}_n\times {\mathbb{C}}^{(m,n)}$ 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 the Siegel-Jacobi disk ${\mathbb{D}}_n\times {\mathbb{C}}^{(m,n)}$.

20 pages Added contents, Added references

References in corpus (3)

• Invariant metrics and Laplacians on Siegel-Jacobi space
• A note on a fundamental domain for Siegel-Jacobi space
• A note on invariant differential operators on Siegel-Jacobi space

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