In mathematics, a Siegel upper half plane is the set of n×n symmetric matrices over the complex number field with their imaginary part being positive definite. The name is for C. L. Siegel.
For example, when n = 1, the Siegel upper half plane is the upper half plane.
There is a group action of the symplectic group
- Sp2n(R)
on the Siegel upper half plane, where
Define
.