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Upper half plane
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).
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