[ksack001]

Ok so is there anyone who can give me a detailed description on how to create the character table of the C2V symmetry molecule? I was able to understand how to calculate all the matrix representations and find the reducible representation. Then I was able to see that all matirx representations were of block diagonal from and from that I got one irreducible representation 1,-1,1,-1 for E,C2,sigmaV, and sigma'v. Now I am left with a two deminsional representation. Then I reduced the two dimensional one by using linear combinations and those matrix representations and I get the A2 and B1 representations. Where does the B2 come from? I know A1 is always 1,1,1,1 I am kind of lost with all of this. I know how to kinda use the character table but he wants us to be able to create it from matrix representations, somebody please help I have searched the internet for hours and there is no detailed description on how to do this that way.