A Partial Cayley Transform of Siegel-Jacobi Disk

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dc.creatorYang, Jae-Hyun
dc.date2005-07-11
dc.date2006-08-24
dc.date.accessioned2026-07-07T09:56:42Z
dc.date.available2026-07-07T09:56:42Z
dc.descriptionLet ${\mathbb H}_g$ 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 Cayley transform of the Siegel-Jacobi disk ${\mathbb D}_g\times {\mathbb C}^{(h,g)}$ onto the Siegel-Jacobi space ${\mathbb H}_g\times {\mathbb C}^{(h,g)}$ which gives a partial bounded realization of ${\mathbb H}_g\times {\mathbb C}^{(h,g)}$ by ${\mathbb D}_g\times {\mathbb C}^{(h,g)}$. We prove that the natural actions of the Jacobi group on ${\mathbb D}_g\times {\mathbb C}^{(h,g)}$ and ${\mathbb H}_g\times {\mathbb C}^{(h,g)}$ are compatible via a partial Cayley transform. A partial Cayley transform plays an important role in computing differential operators on the Siegel-Jacobi disk ${\mathbb D}_g\times {\mathbb C}^{(h,g)}$ invariant under the natural action of the Jacobi group on ${\mathbb D}_g\times {\mathbb C}^{(h,g)}$ explicitly.
dc.description12 pages Added references
dc.identifierhttps://arxiv.org/abs/math/0507216
dc.identifierhttp://arxiv.org/abs/math/0507216
dc.identifierJ. Korean Math. Soc. vol. 45 (2008), No. 3, pp. 781-794.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167071
dc.subjectNumber Theory
dc.subject32-XX
dc.titleA Partial Cayley Transform of Siegel-Jacobi Disk
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