3
$\begingroup$

I'm searching for a reference request where all irreducible representations of the Spin group or of $\mathfrak{so}(n)$ are classified. It seems to be 'well-known' that the Lie algebras correspond to dynkin diagrams in the $B$ and $D$ series, but the exact correspondence is not mentioned. It also appears to be well-known that all representations except the spinorial representation can be found by repeatedly tensoring the lowest-dimensional representation with itself.

However, the only source I can find for all these statements is comments on SE and non-referenced claims on Wikipedia. I guess that shows that this subject is seen as complete or easy. There is a lot of literature about $Spin(3)$, mostly from physics, but I'm struggling to find any real sources about $Spin(n)$ in general. I would appreciate it very much for someone could give me a reference.

$\endgroup$
  • 2
    $\begingroup$ I'm away from my books for a few days, but my recollection is that all of this is in Fulton and Harris's book "Representation theory" $\endgroup$ – Jason DeVito May 10 '18 at 12:53
  • $\begingroup$ @JasonDeVito Thank you! Reading the TOC it seems chapters 18-20 are precisely about special orthogonal and Spin groups. $\endgroup$ – Pepijn de Maat May 10 '18 at 13:17

Your Answer

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

Browse other questions tagged or ask your own question.