State of a Generator in Representation Theory

[Silviu]

Hello! I am reading something about representation theory (just started) and I encountered this: "We will denote the state in the adjoint representation corresponding to an arbitrary generator $X_a$ as |$X_a$>". What is the state of a generator in a certain representation?
Thank you!

 

[Simon Bridge]

They did not talk about the state of a generator.
You have a generator... this can generate a state. They are introducing a notation to help talk about that.
Maybe you need to go back to find the definitions of "state" and "generator", and find out what a generator does?

 

[Silviu]

They did not talk about the state of a generator.
You have a generator... this can generate a state. They are introducing a notation to help talk about that.
Maybe you need to go back to find the definitions of "state" and "generator", and find out what a generator does?

Thank you for your answer. I am still a bit confused. From what I understood generators are part of the Lie Algebra and they can generate the whole Lie Group. For example for SO(2) if S is the generator any rotation by $\alpha$ degrees is written as $e^{i\alpha S}$. So, I understand a generator generates a whole group which usually acts on a vector space. Please let me know if anything I said is wrong. Now, I just don't understand where the idea of state appears in this as I thought that generators are generating a group not states.

 

[Simon Bridge]

I get confusded too and authors can use the same word to refer to slightly different things.
I do not have the context of the passage - but I would see the above as meaning that |A> is a single state belonging to the group that is generated by A.
The passages that follow should include examples that will make the matter clear. If they do not, then get a different book.