Group Theory and Symmetry. Part III: Representations and Character Tables
The article offers information on the use of mathematical aspects of group theory in spectroscopy. It states that dong the symmetry operation changes the two hydrogen atoms, having labels a and b to better see the shift. It says that the matrix multiplication representing the symmetry operation where the C2 symmetry operation as presented by the 2 x 2 matrix.
Ball, David W., "Group Theory and Symmetry. Part III: Representations and Character Tables" (2010). Chemistry Faculty Publications. 148.