How to calculate the group action $ SU (1,1) $ on $ SU (1,1)/U(1) $?
Where $ SU (1,1)/U(1) $ is group quotient.
I know that the general form of a matrix in SU(1,1) is given by
$(\begin{array}{ccc} \alpha & \beta \\ \beta^* & \alpha^* \end{array})$, where $|\alpha|^2 - |\beta|^2 = 1$
Can you suggest articles? or help me solve it?
Please.