Please take a look at the theorem of equation 3.33 http://i.imgur.com/mrWey.jpg
I don't even understand the statement. What does it mean that a function "belongs" to an representation. Also, is the statement correct, or should there be some coefficients in front of each f_i?
I have uploaded this definition, which might be useful http://i.imgur.com/ic80p.jpg
Thanks in advance, Tony Bruguier