|
In mathematics, the upper half plane H is the set of
complex numbers x+iy such that y>0. It is
the domain of many functions of interest in complex analysis, especially modular forms. It is also a model of the hyperbolic plane.
There is a group action of the special linear group SL(2,R) on H defined by
-
The action is transitive and the stabilizer of i is the rotation group
-
Therefore, H = SL(2,R)/SO(2).
|