In the question

Classifying the irreducible representations of $\mathbb{Z}/p\mathbb{Z}\rtimes \mathbb{Z}/n \mathbb{Z}$

the author is talking about irreducible representations of a semi-direct product. Does he mean representations over $\mathbb{C}, \mathbb{Z}, \mathbb{F}_p, \ldots$? Or would the way to construct them be the same?

I'm not sure if it is allowed to re-ask a question. If not. I'm sorry.

  • 1
    $\begingroup$ Over a field ofcharacteristic $p,$ the normal subgroup of order $p$ will act trivially, so you are looking at the irreducible representations of the cyclic group of order $n$. Over fields of other characteristics, one can proceed via Cliffords theorem in a reasonably uniform way, although when the characteristic divides $n$ the theory is a little different, but not too significantly. $\endgroup$ – Geoff Robinson Jul 17 '12 at 18:04
  • $\begingroup$ The old answer is talking about $\mathbb{C}$, though the ideas can be applied more generally. $\endgroup$ – Jack Schmidt Jul 17 '12 at 18:06
  • $\begingroup$ Are there more literature which refers to irred. representations of $\mathbb{Z}/p \mathbb{Z} \rtimes \mathbb{Z}/n \mathbb{Z}$ over $\mathbb{F}_q$ for a prime $q$? I could not find anything in the library. $\endgroup$ – guest Jul 17 '12 at 18:15
  • $\begingroup$ guest look up modular representation theory. $\endgroup$ – JSchlather Jul 17 '12 at 18:56

As Jack Schmidt said: "The old answer is talking about $\mathbb C$, though the ideas can be applied more generally."

(It seems this question has been answered in the comments; in order for the question to be marked as answered, I copied the answer above and made this CW.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.