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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.

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    $\begingroup$ 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" $\endgroup$ Commented May 10, 2018 at 12:53
  • $\begingroup$ @JasonDeVito Thank you! Reading the TOC it seems chapters 18-20 are precisely about special orthogonal and Spin groups. $\endgroup$ Commented May 10, 2018 at 13:17

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