Understanding the Notation of U(p,q) in Group Theory | Wybourne Book Study

[somy]

Hi all.
I'm studying Wybourne book on group theory. I didn't understand this expression:
U(p,q)
I know what U(p+q,C) and U(n) means, but I'm unfamiliar with the notation of the above statement.
Thanks in advance.
Somy

 

[Careful]

I think U(p,q) denotes the group of complex *unitary* transformations A with respect to a metric g with p plusses and q minusses, i.e
A* g A = g

where A* is the standard hermitian conjugate.

 

[somy]

I think so.
Thanks dear Careful!