A Partial Cayley Transform of Siegel-Jacobi Disk

Details A Partial Cayley Transform of Siegel-Jacobi Disk A Partial Cayley Transform of Siegel-Jacobi Disk

2005-07-11

arxiv.org/abs/math/0507216v2

J. Korean Math. Soc. vol. 45 (2008), No. 3, pp. 781-794.

Mathematics

Number Theory

12 pages Added references

Scientific paper

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 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.

Affiliated with

Also associated with

No associations

Rating

A Partial Cayley Transform of Siegel-Jacobi Disk does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Partial Cayley Transform of Siegel-Jacobi Disk, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Partial Cayley Transform of Siegel-Jacobi Disk will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-404706