I can see how this could be confusing, but in mathematics, the phrase “representation theorem” is not specifically about “representation theory”. Wikipedia’s definition is quite broad:
In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure.
The list of examples it gives is probably more useful.
(Adding to the confusion: a famous example of a representation theorem is a corollary of Cayley’s Theorem: for every group G, there is a vector space V such that there is an injective homomorphism G↪GL(V). Ie, the theorem is that every group has a “faithful representation” in the sense of representation theory. So representation theory is built off of a famous example of a representation theorem. But as you can see from the above link, most things labelled “representation theorems” have nothing to do with “representation theory”.)
Yeah, basically this. I realize Woit’s book is not quite the right resource, but it’s just the first thing my brained returned when asked for a resource and it felt spiritually similair enough that I trusted people would get what I was pointing at.
I can see how this could be confusing, but in mathematics, the phrase “representation theorem” is not specifically about “representation theory”. Wikipedia’s definition is quite broad:
The list of examples it gives is probably more useful.
(Adding to the confusion: a famous example of a representation theorem is a corollary of Cayley’s Theorem: for every group G, there is a vector space V such that there is an injective homomorphism G↪GL(V). Ie, the theorem is that every group has a “faithful representation” in the sense of representation theory. So representation theory is built off of a famous example of a representation theorem. But as you can see from the above link, most things labelled “representation theorems” have nothing to do with “representation theory”.)
Yeah, basically this. I realize Woit’s book is not quite the right resource, but it’s just the first thing my brained returned when asked for a resource and it felt spiritually similair enough that I trusted people would get what I was pointing at.