In the context of group theory (in my case, applications to physics), I frequently come across the phrase "the N" of a group, for example "a 24 of SU(5)" or "the 1" (the integer is usually typeset in bold).
My knowledge of group theory is pretty limited. I know the basics, like what properties constitute a group, and I'm familiar with simple cases that occur in physics (e.g. rotation groups SO(2), SO(3), the Lorentz group, SU(2) with the Pauli matrices as a representation), but not much more. I've got a couple of related questions:
- What is meant by "N of a group"?
- Is is just shorthand for an N representation? If so, what exactly is an N representation of a given group? :-)
- How can I work out / write down such a representation concretely, like the Pauli matrices for SU(2)? I'd be grateful for a simple example.
- What does it mean when something "transforms like the N"?