# Irreducible representations of $SO(5)$

I am looking for irreducible representations of the group $SO(5)$ that can be described by a tensor of at most rank two. My own considerations have brought me to the conclusion that there is a dimension 14 symmetric tensor, a dimension 10 antisymmetric tensor, a dimension 5 vector and a one-dimensional scalar singlet. I came to this result by looking at Young-tableaux and calculating the corresponding dimensions.

My question: did I miss something? Is there any other representation I overlooked?

• Yes you are right. Irreps of dimension 1,5,10,14. reassure yourself from Patera & MacKay's "phonebook". Apr 21, 2019 at 14:45