I was trying to deduce character table of C2v. I found that in the Cotton's book Γ1 has been assigned to all +1. I guess E=1 always make sense as character of 1D should always be +1 (I might be wrong in my argument, if so please rectify me) provided there is no mixing. But what about other ΣR[χ(R)]2=h=4 so I can easily take C2=σv=σv' =-1. I just want to know the logic of taking all +1 for Γ1.
Thanks in Advance