# Representation symmetric, antisymmetric or mixed

 P: 47 Hi, While studying Lie groups and in particular the representations I have some trouble with determining whether a representation is a symmetric, antisymmetric or mixed tensor product of the fundamental representations. I'm working with SO(5) to get an understanding about the actual mechanisms. I used Georgi's book Lie Algebras in Particle Physics. Do I understand correctly when saying that a representation, $(a,b) = \bigotimes_a (1,0)\bigotimes_b (0,1)$ is symmetric if b = 0, antisymmetric if a = 0? Or is there more to it? Joris