[ampakine]

This is all confusing the hell out of me. I'll use SO2 as an example. It has 3(3) - 6 = 3 degrees of vibrational freedom and it is in the C_2v point group. I read that if I count how many bonds are left unchanged by each symmetry operation I get a "reducible representation". It then says that when I find out what irreducible representations the reducible representation is made up of "this result tells us that there are two non-degenerate stretching modes, one of A₁ symmetry and one of B₂ symmetry."

I'm lost. I read that the A₁ (or A₂, A₃ etc.) label means symmetric with respect to the principle rotation axis (the z axis) and B₂ is asymmetric with respect to the principle axis. What does this mean with respect to stretching vibrations? Does this mean that A1 is the label for a symmetric stretch and B₂ the label for an asymmetric stretch? If so whats the difference between B₁ and B₂? In this diagram here:

I'm trying to figure out how the character table relates to the diagram but I'm having serious trouble. How does A₁ and B₂ represent 2 stretching modes of vibration?